Calculus originated in the second half of the 17th century with the collaboration of many great minds. It is a branch of advanced mathematics that focuses on Derivatives, Integrals, Limits of Functions, and Infinite Series, as well as related concepts and applications. What’s more, it has been widely applied in fields such as Astronomy, Physics, Engineering Science, Economics, Management Science, Sociology, Biological Sciences, and among many others.
A very well-qualified team consisting of experienced professors from the Department of Mathematics at National University of Defense Technology will guide and accompany you through the mysteries of calculus.
Through the study of this course, you will not only acquire an applicable working knowledge of this riveting field, but also feel the great charm of calculus! Let's start our wonderful learning journey together!
Week One
Promotion Video
Lecture 1. A Preview of Calculus
Lecture 2. Sets and Mappings
Lecture 3. Concepts of Functions and Their Properties
Test for Lecture 2
Test for Lecture 3
Week Two
Lecture 4. Elementary Functions
Lecture 5 Parametric Equations and Ploar Coordinats
Lecture 6 Concepts of limits for functions
Test for Lecture 5
Test for Lecture 6
Test for Lecture 4
Week Three
Lecture 7 Properties and Laws for Limits
Lecture 8 Tests for the Existence of a Limit
Lecture 9 Infinitesimals and Infinite Limits
Test for Lecture 7
Test for Lecture 8
Test for Lecture 9
Week Four
Lecture 10 Concepts of Continuous Functions
Lecture 11 Properties of Continuous Functions
Lecture 12 Concepts of Derivatives
Test for Lecture 10
Test for Lecture 11
Test for Lecture 12
Week Five
Lecture 13 Rules of Derivatives
Lecture 14 Implicit and Parametric Differentiation
Lecture 15 Linear Approximations and Differentials
Test for Lecture 15
Test for Lecture 13
Test for Lecture 14
Week Six
Lecture 16 Rates of Change in Physical Problems
Lecture 17 Antiderivatives and Indefinite Integrals
Lecture 18 Maximum and Minimum values and Fermat Theorem
Test for Lecture 16
Test for Lecture 18
Test for Lecture 17
Week Seven
Lecture 19 Mean Value Theorem
Lecture 20 Indeterminate Forms and L’Hospital’s Rule
Lecture 21 Taylor's Theorem
Test for Lecture 20
Test for Lecture 21
Test for Lecture 19
Week Eight
Lecture 22 How Derivatives Affect the Shape of a Graph
Lecture 23 Curvatures of Plane Curves
Lecture 24 Concepts of Definite Integrals
Test for Lecture 24
Test for Lecture 23
Test for Lecture 22
Week Nine
Lecture 25 Properties of Definite Integrals
Lecture 26 The Fundamental Theorem of Calculus
Lecture 27 Integration by Substitution
Test for Lecture 27
Test for Lecture 25
Test for Lecture 26
Week Ten
Lecture 28 Integration by Parts
Lecture 29 Techniques of Integration
Lecture 30 Improper Integrals
Test for Lecture 29
Test for Lecture 28
Test for Lecture 30
Week Eleven
Lecture 31 Applications to Area and Volume
Lecture 32 Applications to Physics
Lecture 33 Modeling with Differential Equations
Test for Lecture 31
Test for Lecture 33
Test for Lecture 32
Week Twelve
Lecture 34 First-Order Differential Equations
Lecture 35 Second-Order Linear Differential Equations
Lecture 36 Nonhomogeneous Linear Equations
Test for Lecture 34
Test for Lecture 36
Test for Lecture 35
Elementary Mathematics
[1] Zhu Jianmin and Li Jianping, Advanced Mathematics (The 2th edition), Higher Education Press, 2015 (in Chinese)
[2] James Stewart. Calculu: Early Transcendentals (The 8th edition),2014
[3] George B. Thomas, Maurice D. Weir, Joel Hass. Thomas' Calculus(The 14th edition), Pearson,2018