- 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, 8^{th} 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

Redwood College (mostly numerical):

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: