2620Fall 2020
3 Credits

# Multivariable Calculus

This course will cover selected topics from differential and integral calculus of several variables.
Tian Xiang 向田
Course Introduction  Tian Xiang 向田PhD, Tulane University

Tian Xiang is currently an associate professor in the Institute For Mathematical Sciences (IMS) at Renmin University of China. Previously, he received his PhD in mathematics from Tulane University in June 2014. From September 2014 to August 2016, he was a postdoc in IMS at RUC. Since September 2016, he was promoted to be associate at RUC, and he has been a master advisor since September 2018. His research interest mainly lies in analysis of partial differential equations and their applications, nonlinear analysis and dynamical systems; so far, he has published 33 papers in international journals like CVPDE, JDE, Nonlinearity etc. His research has been supported by several funds. He has taught more than 10 courses at RUC since 2015, including Mathematical Analysis II and III, Calculus, Ordinary Differential Equations etc.

##### Interests
• Partial Differential Equations
• Nonlinear Analysis
• Dynamical Systems

#### Multivariable Calculus

UIBE serves as our School of Record
3 Credits

### Course Description

This course will cover selected topics from differential and integral calculus of several variables. Topics include vectors in three dimensions, functions of several variables, partial derivatives, Lagrange multipliers, multiple integrals, line integrals, Green’s Theorem surface integrals, Stokes’ theorem, and applications.

### Courses Outcomes

On successful completion of this course (i.e. by passing this course), a student will be able to

1. Perform calculus operations on vector-valued functions, including derivatives, integrals, curvature, displacement, velocity, acceleration, and torsion.
2. Perform calculus operations on functions of several variables, including partial derivatives, directional derivatives, and multiple integrals.
3. Find extrema and tangent planes.
4. Solve problems using the Fundamental Theorem of Line Integrals, Green’s Theorem, the Divergence Theorem, and Stokes’ Theorem.
5. Apply the computational and conceptual principles of calculus to the solutions of real-world problems.