Introduction to Calculus course
Introduction to Calculus course
Instructor: Huong Tran (VGU)
Email: huong.ttt@vgu.edu.vn
Office: Room 390, Admin Building
VGU New Campus
Office hour: 9.00-11.00 Wednesday mornings
Introduction to Calculus course
Text books
References
1. James Stewart, Essential Calculus, 2007 (Primary textbook).
2. George B. Thomas Jr., Maurice D. Weir, Joel R. Hass, Frank
R. Giordano, Thomass Calculus, 2007, 11th edition.
3. Michael Spivak, Calculus, third edition, Cambridge, 2015
Introduction to Calculus course
Contents
Outline I
1. Introduction
2. Sequences and Series
2.1
2.2
2.3
2.4
Representations for sequences
Convergence and divergence
Limit laws and squeeze theorem
Some known series
3. Limits and continuity
3.1
3.2
3.3
3.4
3.5
Tangent problems
Limit laws
Infinite limits, limits at infinity and asymptotes
Continuous functions
The intermediate value theorem
4. Derivatives and its applications
4.1 Slope of curves, instantaneous velocity, rate of changes;
4.2 Differentiation rules;
Introduction to Calculus course
Contents
Outline II
4.3
4.4
4.5
4.6
4.7
Higher derivatives;
Extreme value theorems, mean value theorems;
Curve sketching;
Linear approximation and Taylor’s series;
Newton iteration method for solution approximating of a
non-linear equation.
5. Integrals, integration techniques and applications
5.1
5.2
5.3
5.4
5.5
5.6
Distance/length, area, and volume problems;
Definite integrals;
Infinite integrals (anti-derivatives), net change theorem;
Fundamental theorem of calculus;
Integration techniques;
Applications.
Introduction to Calculus course
Contents
Relevant courses
▶ Discrete mathematics;
▶ Statistics;
▶ Data structure and Algorithms;
▶ Theoretical Computer Science;
▶ Signal processing.
Introduction to Calculus course
Attendance and exam
Attendance and exam
1. To enable to get the best result, you are recommended to
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attend at least 75% contact hours;
take at least one practice test;
read textbooks frequently;
pose questions as much as possible;
prepare homework/exercises carefully before coming class.
2. Exams and Gradings
▶ Midterm exam: 20% of the overall result. It will be held at the
week 10 of the semester.
▶ Final exam: 80% of the overall result. It lasts in 90 minutes. A
cheat sheet (two-sided A4 sheet) and pocket calculator are
allowed. E-devices are prohibited.