Calculus 1

OVERVIEW

1. Code: PHYS1401, PHYS1801

2. Condition:

• Prerequisite: None

• Previous course: None

3. Property: Compulsory

4. Major/ Training Program: Physics Teacher Education, Physics 

5. Number of credits: 3; Number of periods: 60

DESCRIPTION

This course provides basic knowledge about: the functions of one variable; limits and continuous functions; derivatives, integration; calculations of derivatives, integrals, and applications in solving Physics problems. This course also includes infinite series: numerical series, power series, Fourier series and applications in physics.

OUTCOMES

1. Quality:
   After deriving the problems related to real functions of one variable, the students will enable to master properties of real numbers, concepts and properties of limits, continuity, derivatives, differentials, and integrals of function; and those of numerical series and series of functions.

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

• calculate limits and discuss the continuity of functions.

• compute derivatives, differentials, and integrals of functions.

• test the convergence for a numerical series and find the domain of convergence for a power series.

• solve basic problems including those arising in physics (related rates, electric circuits, work).

CONTENTS

Chapter 1 Functions and Limits

1.1 Functions

1.2 Limits of functions

1.3 Continuity of functions

Chapter 2 Derivatives, differentiation, and applications

2.1 Differentiability, differentiation, derivatives, and high-order derivatives

2.2 Derivatives and differentiation in physics

2.3 Taylor - Maclaurin polynomials

2.4 l’Hospital rules

2.5 Mean value theorems

2.6 Parametric equations

Chapter 3 Integrals and applications

3.1 Indefinite integrals

3.2 Definite integrals

Chapter 4 Series

4.1 Numerical series

4.2 Power series

4.3 Trigonometric series and Fourier series

MATERIALS

1. Nguyen Le Anh, Luong Le Hai,  Nguyen Minh Hai, Nguyen Vu Thu Nhan (2022), Mathematics for Physics. Part 1. Calculus of single-variable functions and Series, to be published.
   Available view here.

2. Do Cong Khanh (2013), Calculus of single-variable functions and series theory, VNU-HCM.

3. To Van Ban (2021), Lectures on Calculus 1 (beta edition), unpublished.
   Available download here.

4. Nguyen Dinh Tri, Ta Van Dinh & Nguyen Ho Quynh (2006), Advanced Mathematics (volume II), Vietnam Education Publishing House.
   Available download here.

5. Vu Thi Hong Thanh (2018), Textbook of Calculus, Vinh University (unpublished).
   Available download here.

6. Bui Xuan Dieu (2019), Lectures on Series - Differential equation - Laplace transform, Hanoi University of Science and Technology (unpublished).
   Available download here.

7. James Stewart (2016), Calculus (8th edition), Cengage Learning.
   Available download here.

8. George B. Thomas, Maurice D. Weir & Joel Hass (2010). Thomas’ calculus (13th edition), Boston, Mass, USA: Addison-Wesley.
   Available download here.

9. Ron Larson & Bruce Edward (2014), Calculus (10th edition), Cengage Learning.
   Available download here.

10. Chris McMullen (2017), Essential Calculus-based Physics Study Guide Workbook, Zishka Publishing.
    Available download: vol 1, vol 2, vol 3.

11. Nguyen Le Anh (2023), Essential calculus for Natural Science students, internal use.
    Available view here.

WEBSITES

• https://www.wolframalpha.com/ 

• https://www.overleaf.com/ 

• https://www.geogebra.org/ 

• https://maxima.sourceforge.io/download.html 

ASSESSMENTS

• Weekly assignments: 10%

• Midterm test: 30%

• Final test: 60%

SCHEDULE (to be updated annually)

1. Week 1: 

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2. Week 2: 

• Topics: 

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