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Dr. Eleftherios Gkioulekas -- faculty web page
Online Lecture Notes on Mathematics
I began hosting my Lecture Notes online since 2006. My goal is to provide free educational resources to anyone around the world that wishes to deeply master Mathematics. It is also my foremost aspiration to preserve a valuable teaching tradition that values and promotes clear mathematical communication skills and a genuine understanding of Mathematics.
Mathematics is inherently beautiful, and naturally attracts the interest of every student that has the inclination to become a good mathematician. Success in mastering mathematics requires, above everything else, a passion/love for the subject. That leads to hard work, patience, and never giving up. It helps, along the way, to have free educational resources that do not dumb down the content and that provide precise writing and complete arguments for proofs, examples, etc, in addition to theory and exercises. This Online Lecture Notes project is my modest contribution towards that end.
Most of the Online Lecture Notes below can be used as course textbooks or for independent study. They include fully solved examples and exercise sets. Most are still work-in-progress and have some rough edges, but many chapters are already in very good shape. If you are a student that has found the notes helpful, or an instructor that has used them in his teaching, or if you found any errors, I would like to hear from you. You may also like Paul's Online Math Notes and The Feynman Lectures on Physics.
For interested faculty, see my power-point presentation concerning this project. This project was made possible thanks to Wanchik's Writer.
Other stuff
Old Notes from UCF
Update Log
- 08/08/2023: Minor correction to CAL 2.5: Series convergence
- 07/26/2023: Minor correction to problem 40a in CAL 2.2: Techniques of Integration
- 06/17/2022: Minor correction to MM2: 1D autonomous systems
- 04/24/2021: Corresponding revisions to DST4: Mappings and Cardinality
- 04/24/2021: Rewrote the Q countable proof sketch in IMP4: Mappings and Functions
- 04/03/2021: Rewrote uniqueness proof for uniqueness of inverse in IMP4: Mappings and Functions
- 03/22/2021: Corrections to IMP4: Mappings and Functions
- 03/22/2021: Corrections to MEE6: Graph Theory. Part 2
- 02/09/2021: Rewrote section on characteristic polynomial in MEE5: Eigenvalues and eigenvectors
- 02/09/2021: Rewrote section on connected graphs in MEE4: Graph Theory. Part 1
- 01/31/2021: Correction to MEE3: Determinants and Linear Systems
- 01/31/2021: Correction to IMP3: Relations
- 01/31/2021: Correction to IMP1: Sets and Logic
- 01/25/2021: Correction to IMP2: Integers
- 01/07/2021: Rewrote and revised IMP2: Integers
- 01/03/2021: Corrections to MEE6: Graph Theory. Part 2
- 01/03/2021: Corrections to MEE5: Eigenvalues and eigenvectors
- 01/03/2021: Corrections to MEE4: Graph Theory. Part 1
- 01/03/2021: Corrections to MEE3: Determinants and Linear Systems
- 01/03/2021: Corrections to DST1: Logic and sets
- 01/03/2021: Corrections to IMP1: Sets and Logic
- 12/28/2020: Correction to MEE1: Brief introduction to Logic and Sets
- 12/24/2020: Correction to IMP1: Sets and Logic
- 10/05/2020: Corrections to ODE7: Laplace Transforms
- 10/05/2020: Corrections to ODE6: Generalized Functions
- 10/05/2020: Corrections to ODE5: Series Solution of Linear Differential Equations
- 09/11/2020: Corrections to ODE5: Series Solution of Linear Differential Equations
- 09/06/2020: Corrections to ODE7: Laplace Transforms
- 09/06/2020: Corrections to ODE6: Generalized Functions
- 09/06/2020: Corrections to ODE5: Series Solution of Linear Differential Equations
- 09/02/2020: Corrections to ODE4: Linear Differential Equations
- 08/26/2020: Corrections to ODE4: Linear Differential Equations
- 08/25/2020: Corrections to ODE5: Series Solution of Linear Differential Equations
- 08/25/2020: Corrections to ODE4: Linear Differential Equations
- 08/25/2020: Corrections to ODE3: Review of Linear Algebra
- 08/09/2020: Revised example in CAL 2.7: Parametric Curves
- 08/09/2020: Corrected typos in CAL 2.6: Power Series
- 07/09/2020: Corrected typos in CAL 2.6: Power Series
- 07/09/2020: Corrected typos in CAL 2.5: Series convergence
- 07/09/2020: Corrected typos in CAL 2.4: Convergent sequences
- 06/28/2020: Updated copyright license to Creative Commons License CC BY-SA 4.0.
- 06/28/2020: More corrections to CAL 2.5: Series convergence
- 06/28/2020: More corrections to CAL 2.4: Convergent sequences
- 06/23/2020: Corrected typos in CAL 2.5: Series convergence
- 06/23/2020: Corrected typos in CAL 2.4: Convergent sequences
- 06/23/2020: Corrected typos in CAL 2.3: Improper Integrals
- 06/13/2020: Corrected typos in CAL 2.2: Techniques of Integration
- 06/07/2020: Corrections to CAL 2.2: Techniques of Integration
- 04/18/2020: Uploaded RA 1.6: Differential Calculus
- 04/12/2020: Added new material to IMP4: Mappings and Functions
- 03/30/2020: Uploaded RA 1.5: Derivatives
- 03/20/2020: Uploaded RA 1.4: Continuity
- 03/15/2020: Uploaded RA 1.3: Limits of functions
- 01/30/2020: Minor corrections to RA 1.1: Structure of the set of real numbers
- 01/26/2020: Uploaded RA 1.2: Limits of sequences and nets
- 01/23/2020: Corrected order axiom on RA 1.1: Structure of the set of real numbers
- 01/08/2020: Uploaded RA 1.B: Brief introduction to Proofs
- 01/08/2020: Uploaded RA 1.A: Brief introduction to Logic and Sets
- 01/08/2020: Made TOC clickable for all Online Lecture Notes
- 01/01/2020: Uploaded RA 1.1: Structure of the set of real numbers
- 01/01/2020: New course: Real Analysis 1
- 07/25/2019: Corrected scanning of CAL 2.2: Techniques of Integration
- 01/20/2019: Updated webpage URL on copyright page.
- 01/20/2019: Partial rescan of Calculus 2 lecture notes.
- 11/24/2018: Corrections to CAL 2.7: Parametric Curves
- 11/24/2018: Corrections to CAL 2.6: Power Series
- 11/24/2018: Corrections to CAL 2.5: Series convergence
- 11/24/2018: Corrections to CAL 2.4: Convergent sequences
- 11/24/2018: Corrections to CAL 2.3: Improper Integrals
- 11/17/2018: Rewrote the trig substitution section in CAL 2.2: Techniques of Integration
- 10/21/2018: Corrections and new trig integral example to CAL 2.2: Techniques of Integration
- 02/12/2018: Corrections to MEE2: Basic Linear Algebra
- 09/19/2017: Revised CAL1.6: Exponentials and Logarithms
- 09/19/2017: Revised CAL3.1: Vectors in 3d
- 09/04/2017: Revised CAL3.6: Vector fields
- 09/04/2017: Revised CAL3.5: Multiple integrals
- 09/04/2017: Revised CAL3.4: Optimization of scalar fields
- 09/04/2017: Revised CAL3.1: Vectors in 3d
- 09/04/2017: Revised CAL1.6: Exponentials and Logarithms
- 09/04/2017: Revised CAL1.5: Differential Calculus
- 09/04/2017: Revised CAL1.2: Limits and Continuity
- 09/04/2017: Revised CAL1.1: Functions and domains
- 06/28/2017: Corrections to CAL3.2: Vector-valued functions
- 06/26/2017: Corrections to CAL3.1: Vectors in 3d
- 06/25/2017: Corrections to CAL3.3: Scalar fields
- 06/25/2017: Corrections to CAL3.5: Multiple integrals
- 06/21/2017: Minor corrections to CAL3.6: Vector fields
- 06/19/2017: Added examples to CAL1.6: Exponentials and Logarithms
- 06/18/2017: Corrections to CAL1.2: Limits and Continuity
- 04/18/2017: Corrected exercise 3i,3j in CAL3.6: Vector fields
- 04/02/2017: Revised implicit derivatives in CAL3.3: Scalar fields
- 03/13/2017: Corrections to CAL3.4: Optimization of scalar fields
- 03/13/2017: Corrections to CAL3.3: Scalar fields
- 02/26/2017: Revised CAL3.6: Vector fields
- 02/26/2017: Revised CAL3.5: Multiple integrals
- 02/26/2017: Revised CAL3.4: Optimization of scalar fields
- 02/09/2017: Corrected problem 33 in CAL3.1: Vectors in 3d
- 02/03/2017: Revised CAL3.3: Scalar fields
- 01/21/2017: Revised CAL3.2: Vector-valued functions
- 01/21/2017: Corrected example in CAL3.1: Vectors in 3d
- 01/14/2017: Rewrote CAL3.1: Vectors in 3d
- 10/11/2016: Fixed out of order pages in MEE3: Determinants and Linear Systems
- 09/24/2016: Revised trig integral examples in CAL 2.2: Techniques of Integration
- 09/20/2016: Corrections to CAL 2.7: Parametric Curves
- 09/20/2016: Corrections to CAL 2.6: Power Series
- 09/20/2016: Corrections to CAL 2.5: Series convergence
- 09/20/2016: Corrections to CAL 2.2: Techniques of Integration
- 09/11/2016: Revision to CAL 2.3: Improper Integrals
- 09/11/2016: Corrections to CAL 2.2: Techniques of Integration
- 09/03/2016: Rewrote section on rational integrals in CAL 2.2: Techniques of Integration
- 09/01/2016: Revision to CAL 2.2: Techniques of Integration
- 12/14/2015: Rewrote CAL1.5: Differential Calculus
- 11/21/2015: Minor correction to CAL1.4: Derivatives
- 11/21/2015: Minor correction to CAL1.3: Asymptotes
- 11/21/2015: Minor correction to CAL1.2: Limits and Continuity
- 09/19/2015: Revised DST6: Formal Languages and Automata
- 09/13/2015: Revised DST4: Mappings and Cardinality
- 09/13/2015: Minor correction to DST3: Relations
- 09/13/2015: Minor correction to IMP3: Relations
- 09/12/2015: Revised DST2: Basic number theory
- 09/12/2015: Revised DST5: Basic graphs
- 09/12/2015: Revised IMP1: Sets and Logic
- 09/12/2015: Revised DST1: Logic and sets
- 09/12/2015: Revised DST7: Turing machines
- 09/07/2015: Minor correction to MEE5: Eigenvalues and eigenvectors
- 09/07/2015: Minor correction to LIN4: Eigenvalues and Eigenvectors
- 09/05/2015: Major revision of MEE6: Graph Theory. Part 2
- 08/30/2015: Revised LIN4: Eigenvalues and Eigenvectors
- 08/30/2015: Revised MEE5: Eigenvalues and eigenvectors
- 08/30/2015: Revised MEE4: Graph Theory. Part 1
- 08/22/2015: Revised LIN4: Determinants and Linear Systems
- 08/22/2015: Revised LIN3: Basic Linear Algebra
- 08/22/2015: Revised MEE3: Determinants and Linear Systems
- 08/22/2015: Revised MEE2: Basic Linear Algebra
- 08/18/2015: Minor correction to LIN1: Brief introduction to Logic and Sets
- 08/18/2015: Minor correction to MEE1: Brief introduction to Logic and Sets
- 04/13/2015: Fixed out of order pages on DST6: Formal Languages and Automata
- 02/23/2015: Uploaded DST7: Turing machines
- 02/16/2015: Added example to DST1: Logic and sets
- 02/16/2015: Added example to IMP1: Sets and Logic
- 02/15/2015: Uploaded DST6: Formal Languages and Automata
- 02/15/2015: Uploaded DST5: Basic graphs
- 02/01/2015: Updated copyright notices on all notes.
- 12/25/2014: Uploaded DST4: Mappings and Cardinality
- 12/25/2014: Revised some examples in IMP4: Mappings and Functions
- 12/25/2014: Minor correction to IMP3: Relations
- 12/20/2014: Uploaded DST3: Relations
- 12/20/2014: Uploaded DST2: Basic number theory
- 12/20/2014: Uploaded DST1: Logic and sets
- 12/20/2014: New course: Discrete Structures
- 12/20/2014: Rewrote IMP1: Sets and Logic
- 11/25/2014: Corrected parabola examples in PRE8: Conic sections
- 10/22/2014: Minor correction to PRE4: Trigonometric equations and inequalities
- 09/23/2014: Added some proofs to PRE3: Trigonometric identities
- 09/21/2014: Correction to PRE3: Trigonometric identities
- 09/07/2014: Correction and revision to PRE2: Trigonometric functions
- 08/28/2014: Revised PRE4: Trigonometric equations and inequalities
- 08/28/2014: Rewrote beginning of PRE2: Trigonometric functions
- 08/28/2014: Rewrote PRE1: Review of geometry
- 08/25/2014: Rewrote graphing of trig functions in PRE2: Trigonometric functions
- 08/23/2014: Added examples to PRE3: Trigonometric identities
- 08/23/2014: Added examples to PRE2: Trigonometric functions
- 08/09/2014: Uploaded corrections to ODE7: Laplace Transforms
- 08/06/2014: Uploaded important corrections to problem 3 in ODE7: Laplace Transforms
- 08/04/2014: Correction to ODE7: Laplace Transforms
- 08/01/2014: Minor corrections to ODE5: Series Solution of Linear Differential Equations
- 08/01/2014: New introduction added to ODE6: Generalized Functions
- 07/26/2014: Revised ODE4: Linear Differential Equations
- 07/26/2014: Revised ODE2: First-order ODEs
- 07/13/2014: Minor correction to CAL1.4: Derivatives
- 06/12/2014: Major revisions to ODE6: Generalized Functions
- 06/12/2014: Major revisions to ODE2: First-order ODEs
- 06/11/2014: Minor corections to CAL1.2: Limits and Continuity
- 06/07/2014: Minor correction to CAL1.1: Functions and domains
- 06/07/2014: Major revisions to ODE7: Laplace Transforms
- 04/24/2014: Uploaded ODE7: Laplace Transforms
- 03/23/2014: Uploaded ODE6: Series Solution of Linear Differential Equations
- 02/14/2014: Uploaded ODE5: Generalized Functions
- 01/20/2014: Minor corrections to ODE2: First-order ODEs
- 01/19/2014: Uploaded ODE4: Linear Differential Equations
- 01/19/2014: Added material to ODE3: Review of Linear Algebra
- 01/05/2014: Uploaded ODE3: Review of Linear Algebra
- 01/05/2014: Uploaded ODE2: First-order ODEs
- 01/05/2014: Uploaded ODE1: Introduction to ODEs
- 01/05/2014: New course: Ordinary Differential Equations
- 11/23/2013: Uploaded CAL 2.7: Parametric Curves
- 11/17/2013: Completed CAL 2.6: Power Series
- 11/14/2013: Uploaded CAL 2.6: Power Series
- 10/06/2013: Uploaded CAL 2.5: Series convergence
- 10/06/2013: Uploaded CAL 2.4: Convergent sequences
- 10/02/2013: Added problems to CAL 2.3: Improper Integrals
- 09/22/2013: Add problem 25 to CAL 2.2: Techniques of Integration
- 09/01/2013: Added problems to CAL 2.2: Techniques of Integration
- 08/24/2013: Uploaded CAL 2.3: Improper Integrals
- 08/24/2013: Uploaded CAL 2.2: Techniques of Integration
- 08/24/2013: Uploaded CAL 2.1: Integrals -- Calculus 1 review
- 08/24/2013: New course: Calculus 2
- 07/05/2013: Rewrote CAL1.3: Asymptotes
- 06/24/2013: Revised trig functions limits on CAL1.2: Limits and Continuity
- 06/08/2013: Revised limits on CAL1.2: Limits and Continuity
- 06/05/2013: Revised limits definition on CAL1.2: Limits and Continuity
- 06/04/2013: Minor correction to CAL1.1: Functions and domains
- 06/01/2013: Rewrote CAL1.1: Functions and domains
- 05/29/2013: Rewrote CAL1.4: Derivatives
- 03/31/2013: Revised CAL1.8: Introduction to integrals
- 03/16/2013: Reorganized notes for Math for Electrical Engineers
- 03/16/2013: Added new section to IMP3: Relations
- 03/15/2013: More revisions to IMP3: Relations
- 03/11/2013: Revised IMP3: Relations
- 01/28/2013: Revised MEE2: Basic Linear Algebra
- 01/28/2013: Minor correction to MEE1: Brief introduction to Logic and Sets
- 01/21/2013: Reorganized notes for Intro Mathematics Proof
- 01/11/2013: Reorganized notes for Math for Electrical Engineers
- 11/01/2012: Uploaded LIN6: Vector Spaces -- Theory Questions
- 10/06/2012: Corrected problem 32 in LIN3: Basic Linear Algebra
- 10/06/2012: Corrected problem 32 in MEE3: Basic Linear Algebra
- 08/06/2012: Minor corrections to LIN3: Basic Linear Algebra
- 08/06/2012: Minor corrections to LIN2: Brief introduction to Proofs
- 08/06/2012: Minor corrections to LIN1: Brief introduction to Logic and Sets
- 08/06/2012: Minor corrections to MEE3: Basic Linear Algebra
- 08/06/2012: Minor corrections to MEE2: Brief introduction to Proofs
- 08/06/2012: Minor corrections to MEE1: Brief introduction to Logic and Sets
- 07/23/2012: Revised MM5: Limit cycles
- 07/23/2012: Revised MM4: Nonlinear autonomous systems
- 07/22/2012: Revised MM3: Linear autonomous systems
- 07/22/2012: Revisions and corrections to exercises 5,6,7 in MM2: 1D autonomous systems
- 07/16/2012: Revised MM2: 1D autonomous systems
- 07/16/2012: Revised MM1: Introduction to autonomous dynamical systems
- 06/17/2012: Uploaded LIN5: Vector Spaces
- 06/17/2012: Uploaded LIN4: Eigenvalues and Eigenvectors
- 06/17/2012: Uploaded LIN3: Basic Linear Algebra
- 06/17/2012: Uploaded LIN2: Brief introduction to Proofs
- 06/17/2012: Uploaded LIN1: Brief introduction to Logic and Sets
- 06/17/2012: New course: Linear Algebra
- 06/17/2012: Reorganized notes for Math for Electrical Engineers
- 06/16/2012: Rescanned MM6: Center manifold reduction
- 04/18/2012: Revised MM6: Center manifold reduction
- 04/11/2012: Uploaded MM6: Center manifold reduction
- 01/19/2012: Minor correction to MM1: Introduction to autonomous dynamical systems
- 09/14/2011: Corrected example in CA2: Equations and Inequalities (Auxiliary substitution)
- 07/30/2011: Minor revision to CA4: Functions
- 07/30/2011: Major revision to CA2: Equations and Inequalities (equations with radicals)
- 07/26/2011: Major revision to CA2: Equations and Inequalities (binomial eqs; sign tables)
- 07/09/2011: Corrected examples in CA7: Exponentials and Logarithms
- 06/07/2011: Rescanned CAL3.6: Vector fields (removed the lines)
- 06/03/2011: Minor revision to IMP4: Relations and Mappings.
- 06/03/2011: Major revision to IMP3: Real numbers
- 06/03/2011: Major revision to IMP2: Integers
- 06/03/2011: Major revision to IMP1: Sets and Logic
- 05/30/2011: Uploaded Calculus 3 book.
- 05/29/2011: Uploaded CAL3.6: Vector fields
- 05/29/2011: Uploaded CAL3.5: Multiple integrals
- 05/29/2011: Uploaded CAL3.4: Optimization of scalar fields
- 05/29/2011: Uploaded CAL3.3: Scalar fields
- 05/04/2011: Corrected log equation examples in CA7: Exponentials and Logarithms
- 04/07/2011: Minor revisions and corrections to CA4: Functions
- 04/02/2011: Corrected Napier flowchart in CAL1.6: Exponentials and Logarithms
- 03/25/2011: Corrected problem 15d in CAL1.4: Derivatives
- 03/24/2011: Corrected problem 10c in CAL1.4: Derivatives
- 03/06/2011: Corrected problem 7j in CAL1.4: Derivatives
- 03/02/2011: Minor revision to CA3: Systems of Equations
- 03/02/2011: Corrections to CA2: Equations and Inequalities (abs. value inequalities)
- 02/09/2011: Revised CAL1.5: Differential Calculus (Added Rolle/MVT examples)
- 02/04/2011: Minor update to CA3: Systems of Equations (deleted redundant page)
- 02/04/2011: Major revision to CA7: Exponentials and Logarithms (added examples)
- 02/01/2011: Major revision to CA5: Graphing functions (added examples)
- 01/26/2011: Major revision to CA4: Functions (more examples/clarity)
- 01/26/2011: Major revision to CA3: Systems of Equations (revised 3x3 systems)
- 01/26/2011: Same correction to BA2: Equations and Inequalities
- 01/26/2011: Corrected CA2: Equations and Inequalities (polynomial equations example)
- 01/22/2011: Corrected domains example in BA3: Functions
- 01/22/2011: Corrected domains example in CA4: Functions
- 01/22/2011: Corrected domains example in CAL1.1: Functions and domains
- 01/14/2011: Revised CAL1.1: Functions and domains
- 01/14/2011: Revised CA4: Functions
- 01/14/2011: Revised CA2: Equations and Inequalities
- 01/14/2011: Revised CA1: Review of Sets
- 01/09/2011: Uploaded BA3: Functions
- 01/09/2011: Uploaded BA2: Equations and Inequalities
- 01/09/2011: Uploaded BA1: Review of sets
- 01/09/2011: New course: Business Algebra
- 12/30/2010: Uploaded CAL3.2: Vector-valued functions
- 12/13/2010: Corrected problem 13b on CAL1.2: Limits and Continuity
- 12/01/2010: Uploaded CAL3.1: Vectors in 3d
- 12/01/2010: New course: Calculus 3.
- 11/10/2010: Corrected problem 6a in CAL1.6: Exponentials and Logarithms
- 10/21/2010: Revised CAL1.2: Limits and Continuity (updated problem 11)
- 09/16/2010: Corrected problem 2d in CAL1.2: Limits and Continuity.
- 09/16/2010: Revised CAL1.2: Limits and Continuity (solution to problem 1)
- 08/31/2010: Revised CAL1.5: Differential Calculus (Fermat theorem)
- 08/31/2010: Revised CAL1.2: Limits and Continuity (trig limits)
- 08/29/2010: Revised CAL1.2: Limits and Continuity (finite limits)
- 08/29/2010: Revised CAL1.2: Limits and Continuity (limits to infinity)
- 08/29/2010: Revised CAL1.2: Limits and Continuity (limit definition)
- 08/14/2010: Moved books to local web server.
- 06/09/2010: Minor revision to IMP1: Sets and Logic
- 05/03/2010: Incorporated CA lecture note corrections to lulu.com
- 05/03/2010: Revised CA3: Systems of Equations (added solved examples)
- 05/03/2010: Revised CA2: Equations and Inequalities (added solved examples)
- 05/03/2010: Reordered CA notes
- 05/02/2010: Incorporated IMP lecture note corrections to lulu.com
- 05/02/2010: Minor revision to IMP5: Rational and Irrational numbers
- 05/02/2010: Posted MM lecture notes on lulu.com
- 05/02/2010: Incorporated PRE lecture note corrections to lulu.com
- 05/02/2010: Minor revision to PRE8: Conic sections
- 05/02/2010: Minor revision to MM5: Limit cycles
- 04/25/2010: Revised PRE8: Conic sections (added hyperbola)
- 04/25/2010: Minor revision to PRE7: Sequences and series
- 04/25/2010: Minor revision to PRE6: Vectors
- 04/21/2010: Minor revision to MM5: Limit cycles
- 04/21/2010: Minor revision to MM4: Nonlinear autonomous systems
- 04/21/2010: Minor revision to PRE5: Application to Triangles
- 04/20/2010: Revised MM5: Limit cycles (added Hopf bifurcation)
- 04/14/2010: Revised MM5: Limit cycles (added orbital stability)
- 04/05/2010: Uploaded MM5: Limit cycles
- 03/23/2010: Minor revision to PRE4: Trigonometric equations and inequalities
- 03/20/2010: Posted PRE notes on lulu.com
- 03/20/2010: Uploaded PRE8: Conic sections
- 03/17/2010: Uploaded PRE7: Sequences and series
- 03/17/2010: Uploaded PRE6: Vectors
- 03/16/2010: Minor revisions to PRE4: Trigonometric equations and inequalities
- 03/16/2010: Minor revision to MM4: Nonlinear autonomous systems
- 03/16/2010: Corrected problem 6 in MM3: Linear autonomous systems
- 03/05/2010: Incorporated CAL1 lecture note corrections to lulu.com (fixed trig identities)
- 03/02/2010: Revised MM4: Nonlinear autonomous systems (now complete)
- 03/02/2010: Corrected Trigonometric identities (the tan(2a) identity)
- 03/01/2010: Corrected product to sum identity in PRE3: Trigonometric identities
- 03/01/2010: Uploaded MM4: Nonlinear autonomous systems (incomplete)
- 02/24/2010: Corrected Trigonometric identities. (the cos(2a) = 1-2sin^2(a) identity)
- 02/23/2010: Uploaded PRE5: Application to Triangles
- 02/19/2010: Corrected problem 5 in MM1: Introduction
- 02/19/2010: Revised MM2: 1D autonomous systems (pitchfork proof)
- 02/14/2010: Uploaded PRE4: Trigonometric equations and inequalities
- 01/31/2010: Incorporated BC lecture note corrections to lulu.com
- 01/31/2010: Revised BC8: Multivariate Calculus
- 01/31/2010: Other minor revisions to PRE2: Trigonometric functions
- 01/31/2010: Corrected problem 2a in PRE2: Trigonometric functions
- 01/29/2010: Fixed sign error in problem 7 in MM2: 1D autonomous systems
- 01/26/2010: Uploaded MM3: Linear autonomous systems
- 01/18/2010: Revised MM1: Introduction to autonomous dynamical systems
- 01/17/2010: Incorporated CAL1 lecture note corrections to lulu.com
- 01/16/2010: Uploaded MM2: 1D autonomous systems
- 01/15/2010: Uploaded MM1: Introduction to autonomous dynamical systems
- 01/12/2010: New course: Mathematical Modeling
- 12/20/2009: Updated CAL1.8: Introduction to integrals (new proof of FTC)
- 12/14/2009: Corrected CAL1.8: Introduction to integrals (substitution examples)
- 12/05/2009: Uploaded PRE3: Trigonometric identities
- 11/28/2009: Uploaded PRE2: Trigonometric functions
- 11/28/2009: Uploaded PRE1: Review of geometry
- 11/28/2009: New course: Precalculus
- 11/28/2009: Minor revisions to CAL1.7: Other Inverse Functions
- 11/23/2009: Corrected convexity of gen. log in CAL1.6: Exponentials and Logarithms
- 11/18/2009: Revised CAL1.6: Exponentials and Logarithms (added page: gen. exp. function)
- 11/11/2009: Corrected derivative of lnx rule at CAL1.6: Exponentials and Logarithms
- 11/11/2009: Corrected problems 11a, 11c, 11d in CAL1.6: Exponentials and Logarithms
- 11/05/2009: Minor revision to CAL1.6: Exponentials and Logarithms (inverse func. flowchart)
- 11/01/2009: Minor revision to CAL1.2: Limits and Continuity (Bolzano thm)
- 10/30/2009: Corrected convexity definition in CAL1.5: Differential Calculus
- 10/21/2009: Corrected problems 9c, 10b in CAL1.4: Derivatives
- 10/10/2009: Posted CAL1 lecture notes on lulu.com
- 10/07/2009: Uploaded CAL1.8:Introduction to integrals
- 10/04/2009: Uploaded Trigonometric identities
- 09/27/2009: Uploaded CAL1.7: Other Inverse Functions
- 09/22/2009: Minor revisions to CAL1.2: Limits and Continuity (trig. limits)
- 09/13/2009: Uploaded CAL1.6: Exponentials and Logarithms
- 09/08/2009: Uploaded CAL1.5: Differential Calculus
- 09/07/2009: Uploaded CAL1.4: Derivatives
- 08/24/2009: Uploaded CAL1.3: Asymptotes
- 08/24/2009: Uploaded CAL1.2: Limits and Continuity
- 08/24/2009: Uploaded CAL1.1: Functions and domains
- 08/24/2009: Uploaded CAL1.0: Review of inequalities
- 08/24/2009: New course: Calculus 1.
- 08/24/2009: Reorganized links.
- 07/10/2009: Incorporated IMP lecture note corrections to lulu.com
- 07/08/2009: Corrected problem 16 on IMP4: Relations and Mappings.
- 07/06/2009: Corrected problem 9d on IMP4: Relations and Mappings.
- 07/06/2009: Corrected problem 7 on IMP4: Relations and Mappings.
- 07/06/2009: Deleted problem 5c on IMP4: Relations and Mappings.
- 07/02/2009: Minor corrections to IMP3: Real numbers
- 06/29/2009: Corrected problem 7f on IMP3: Real numbers
- 06/29/2009: Minor corrections to IMP3: Real numbers
- 06/29/2009: Corrected problem 8 on IMP2: Integers
- 06/27/2009: Posted BC lecture notes on lulu.com
- 06/27/2009: Posted MEE lecture notes on lulu.com
- 06/27/2009: Posted CA lecture notes on lulu.com
- 06/19/2009: Corrected problem 5a on IMP2: Integers.
- 06/19/2009: Corrected problem 14h on IMP1: Sets and Logic.
- 06/10/2009: Corrected problems 12d and 18 on IMP1: Sets and Logic
- 06/09/2009: Minor revisions to CA6: Exponentials and logarithms
- 06/09/2009: Minor revisions to CA4: Graphing functions
- 06/09/2009: Minor revisions to CA3: Functions
- 06/09/2009: Minor revisions to CA2: Equations and Inequalities
- 06/09/2009: Minor revisions to MEE5: Graph Theory
- 06/05/2009: Minor revisions to MEE3: Eigenvalues and their applications.
- 06/05/2009: Minor revisions to MEE2: Applications of linear systems
- 06/05/2009: Minor revisions to MEE1: Matrices and linear systems
- 06/02/2009: Posted IMP lecture notes on lulu.com
- 06/01/2009: Uploaded IMP5: Rational and Irrational numbers
- 06/01/2009: Uploaded IMP4: Relations and Mappings
- 05/25/2009: Uploaded IMP3: Real numbers
- 05/25/2009: Uploaded IMP2: Integers
- 05/23/2009: Uploaded IMP1: Sets and Logic
- 05/23/2009: New course: Intro Mathematics Proof
- 04/14/2009: Corrected problem 16 in CA5: Polynomial functions.
- 04/09/2009: Added missing page on Hamiltonian graphs in MEE5: Graph Theory
- 04/09/2009: Corrected definition of Eulerian graph in MEE5: Graph Theory
- 03/24/2009: Uploaded Interstellar Travel notes
- 03/07/2009: Uploaded CA7: Systems of Equations
- 03/07/2009: Uploaded CA6: Exponentials and logarithms
- 03/07/2009: Uploaded CA5: Polynomial functions
- 02/27/2009: Uploaded CA4: Graphing functions
- 02/19/2009: Uploaded MEE5: Graph Theory
- 02/19/2009: Uploaded MEE4: Review of Sets
- 02/19/2009: Fixed minor sign error in pp. 2-4 of MEE2
- 02/01/2008: Uploaded CA0: Review of Intermediate Algebra
- 01/20/2009: Uploaded MEE3: Eigenvalues and their applications
- 01/19/2009: Uploaded MEE2: Applications of linear systems
- 01/14/2009: Uploaded MEE1: Matrices and linear systems
- 01/14/2009: New course: Math for Electrical Engineers
- 12/23/2009: Uploaded CA3: Functions
- 12/23/2009: Uploaded CA2: Equations and Inequalities
- 12/23/2009: Uploaded CA1: Review of Sets
- 12/23/2009: New course: College Algebra
- 08/28/2008: Uploaded BC8: Multivariate Calculus
- 08/28/2008: Uploaded BC7: Consumer and Producer Surplus
- 08/28/2008: Uploaded BC6: Introduction to Integrals
- 08/26/2008: Uploaded BC5: Optimization
- 08/19/2008: Uploaded BC4: Curve Analysis
- 08/19/2008: Uploaded BC3: Review of sign charts
- 08/19/2008: Uploaded BC2: Derivatives
- 08/19/2008: Uploaded BC1: Limits
- 08/19/2008: New course: Business Calculus