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Teaching Calculus with MATLAB
- Allow your students to effortlessly switch among visual, numerical, and algebraic representations of calculus concepts.
- Shift emphasis from manipulative skills to fundamental calculus ideas.
- Improve students’ engagement and concept retention by exploring more realistic problems earlier.
- Introduce your students to professionally developed, rigorously tested, and fully documented mathematical modeling software that will help them throughout their studies and careers.
- Communicate mathematical ideas using a single notebook that includes explanatory text, formulas, pictures, as well as MATLAB commands, outputs and graphics.
Some Benefits of Using Computation in Calculus Courses:
Research shows that the thoughtful inclusion of computation in calculus courses (Murphy, 2006) provides a dynamic, hands-on, learning environment (Vasquez, 2015), promotes concept understanding (Awang, Zakaria, 2013, Leng et. al. 2009), keeps students engaged (Colonna, Easley, 2011), and increases their competence and confidence (Merriweather, Tharp, 1999).
Free Course Materials:
Texas A&M University (symbolic, using Early Transcendentals, 8th edition):
- Calculus 1 (Chapters 2-6, 10-12)
- Calculus 2 (Chapters 5-7, 10-11)
- Calculus 3 (Chapters 12-16)
University of Maryland (symbolic):
- Calculus1: Functions, Plotting, Differentiation and Integration
- Calculus2: (Math 241): MATLAB Materials
University of Ohio (mixed symbolic and numerical):
- Math Homework with MATLAB (general link)
- Calculus I Homework
- Calculus II Homework
- Calculus III Homework
- Workbook Supplement for Calculus, Differential Equations, and Linear Algebra
Other Calculus course materials (numerical):
- Teaching Calculus with MATLAB University of Stuttgart
- Bridge to Mathematics Northeastern University
Example Lecture Materials:
Essential Calculus Lectures with MATLAB: Functions, Limits, Continuity, Derivatives and Integrals (Download)
Video Lectures:
Pre-Calculus and Algebra Lectures:
- Solving Algebraic Equations Symbolically (11:54)
- Solving Systems of Algebraic Equations Symbolically (12:11)
Calculus Lectures:
Note: since “inline” will be discontinued, to follow through the videos in the links below replace function definitions like “f=inline('sin(x)/x','x');” with function definitions like “syms x f(x); f(x)=sin(x)/x;”
- Limits using MATLAB (6:31)
- Derivatives using MATLAB (6:26)
- Evaluating Derivatives at a point (5:37)
- Partial Derivatives using MATLAB (8:37)
- Indefinite and Definite Integrals (9:10)
- Calculus Operations with MATLAB (22:34)
Differential Equations and Linear Algebra:
- Learn Differential Equations
- Differential Equations and Linear Algebra Course by Gilbert Strang (MIT)
- Solve ODEs in MATLAB (MIT Courseware)
- Solving Ordinary Differential Equations with MATLAB (self paced course)
Curriculum Usage Examples:
- Mathematics Undergraduate Students at the University of Oxford Use MATLAB for Symbolic Computation and Problem Solving
- Manchester Metropolitan University Students Vote Math Best Overall Course Following Adoption of MATLAB
- Chalmers University of Technology Integrates MATLAB Throughout Core Mathematics Curriculum
- Using MATLAB to Teach Problem-Solving Techniques to First-Year Liberal Arts Students
MATLAB Documentation and Examples for Calculus:
An introduction to Symbolic Math Toolbox utilities for calculus:
- Introduction to Symbolic Math via hands-on practice sessions and demonstrations
- Introduction to Symbolic Math with MATLAB
- Solving Nonlinear Equations with MATLAB
- Solving Ordinary Differential Equations with MATLAB
- Introduction to Linear Algebra with MATLAB
- Introduction to Statistical Methods with MATLAB
- Symbolic Toolbox Cheat Sheet
- Collection of Calculus utilities
Common calculus topics in the Symbolic Math Toolbox documentation:
- Limits
- Differentiation
- Integration
- Taylor Series
- Solve Differential Equations
- Ordinary Differential Equations
Other Symbolic Math Toolbox examples:
- Analytical Plotting with Symbolic Math Toolbox
- Find Asymptotes, Critical and Inflection Points
- List of all examples
Numerical functions commonly used in calculus:
More MATLAB Information:
Learn MATLAB in 2 hours:
- MATLAB Onramp, a free, interactive tutorial (and other self-paced courses)
Free Auto Grading:
MATLAB in Industry:
Get MATLAB:
