HCM UT – HCM NU Faculty of Applied Science Department of Math Applied

Ho Chi Minh City, 20 February 2010

Syllabus

006002 – GIẢI TÍCH 2 Credit Class Hours Overall Grade

: 4 (3 – 2 – 5) 75 Theory: 45 Exercises: 30 Consultation: 1 class hours per week par TA : Midterm exam 20% Writeen (60') Homework 30% Writeen (Class Test + Assignment) Final exam 50% Writeen exam (120’)

Course outline: This course is oriented to engineering students and others who require a working knowledge of calculus. Topics to be covered include differential and integration calculus of function of several variables and theory of numeric and power series. The focus will be on understanding the solving techniques and the engineering meaning of divers problems, and not on rigorous profs.

Textbook: Softcopy + Hardcopy [1]

James Stewart, Calculus Early Transcendentals, 6th edition, Thomson & Brooks Cole, 2008

Lecturer: • PhD. Nguyen Quoc Lan (nqlan@hcmut.edu.vn) • TA: MS. Nguyen Hong Loc

- Faculty of Applied Science - Faculty of Applied Science

Course contents: Chapter 1: Function of several variables. Partial derivatives. Chapter 2: Maximum and minimum values of function of several viables Chapter 3: Double and Triple Integrals. Chapter 4: Line and Surface Integrals. Chapter 5: Numeric and power series.

Outcome: After this couse, students are expected to be able to: 1/ Find partial derivatives, directive derivatives. 2/ Find maximum, minimum values of function of several viables 3/ Evaluate double and triple integrals. 4/ Evaluate line (1st and 2nd type) integrals. 5/ Evaluate surface (1st and 2nd type) integrals. 6/ Study the convergence, divergence of numeric and power series.

Approximate Schedule: Week Content 1 Chapter 1: Partial derivatives 1.1 Function of several variables. 1.2 Partial derivatives 2 1.3: Directive derivative PĐT, Mẫu 2005-ĐC

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Syllabus

Week 3 4 5 6 7 8 9 10 11 12 13 14 15

PĐT, Mẫu 2005-ĐC

Content 1.4: Linear approximation. Chapter 2: Maximum and minimum values 2.1: Neccesary and Sufficient condition 2.2: Maximum and minimum values in closed domain Chapter 3: Double and Triple Integrals 3.1: Double Integral over rectangle 3.2: Double Integral over disk 3.3: Application 3.4: Triple Integral over box. 3.5: Cylindrical coordinates. 3.6: Spherical coordinates 3.7: Application MIDTERM EXAM Chapter 4: Line and Surface Integral 4.1: Line Integrals (1st and 2nd type) 4.2: Green theorem. Independence of path 4.3: Application 4.4: Surface Integral (1st and 2nd type) 4.5: Stoke and Divergence theorem. 4.6: Application Chapter 5: Series 5.1: Numeric series 5.2: Positive series 5.2: Alternative series 5.3: Power series (Reserve) Review --------------- END ----------------------

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