Calculus 2

This course provides basic knowledge about: Functions of two or more variables and their derivates, their local maxima and minima; first-order differential Equations and second-order differential equations; systems of first-order differential equations with constant coefficients. This course detailed multiple integrals (specific double and triple integrals); line integrals and surface integrals. This course requires students to acquire the ability to compute integral for application in solving physical problems.

OUTCOMES

Quality:

Knowing first and second-order linear differential equations and the system of first-order linear differential equations and solving them.
Understanding partial derivatives, differentiation, multiple integrals, line and surface integrals.

Competence:
By the end of this module, students will be able to:

calculate partial derivatives, double and triple integrals, and line and surface integrals.
solve first- and second-order differential equations, especially linear differential equations.

Chapter 1 Calculation of multi-variable functions

1.1 Multi-variable functions, limits, and continuity

1.2 Differentiation of multivariable functions

1.3 Extremes

Chapter 2 Multiple integrals

2.1 Double integrals

2.2 Triple integrals

2.3 Variable transformation in multiple integrals

Chapter 3 Line integrals

3.1 Line integrals

3.2 Vector field, work, circulation, and flux

3.3 Path independence of line integrals, potential functions, and conserved field

3.4 Green's theorem

Chapter 4 Surface integrals

4.1 Surface and area

4.2 Surface integrals

4.3 Stokes' theorem

4.4 Divergence theorem and unified theory

Chapter 5 Differential equations

5.1 First-order differential equations

5.2 Second-order differential equations

MATERIALS

Luong Le Hai, Nguyen Minh Nhut, Nguyen Le Anh, Nguyen Vu Thu Nhan (2023), Mathematics for Physics. Part 2. Calculus of multi-variable functions and differential equations, HCMUE Publishing.
Available view here.
Do Cong Khanh (2016), Calculus of multivariable functions and differential equations, VNU-HCM.
James Stewart (2001), Calculus, Cengage Learning.
Ron Larson & Bruce Edward (2014), Calculus (10th edition), Cengage Learning.
Chris McMullen (2017), Essential Calculus-based Physics Study Guide Workbook, Zishka Publishing.

WEBSITES

ASSESSMENTS

Weekly assignments: 10%
Midterm test: 30%
Final test: 60%

SCHEDULE (to be updated annually)

Week 1:

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