- 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 leading-edge mathematical 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:

Calculus 1 at Texas A&M University (symbolic):

Calculus 2 at Texas A&M University (symbolic):

Calculus 3 at Texas A&M University (symbolic):

University of Maryland (symbolic):

- Calculus1: Functions, Plotting, Differentiation and Integration
- Calculus2: (Math 241): Matlab Materials

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 1 lectures with MATLAB: an example (download):

- Functions (preview)
- Limits (preview)
- Continuity (preview)
- Derivatives (preview)
- Integrals (preview)

### 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)=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:

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: