HCM UT – HCM NU Faculty of Applied Science Department of Math Applied
Ho Chi Minh City, 21 January 2011
Syllabus
006001 – GIẢI TÍCH 1 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') Test + Activities 15% (Class Test + Attendance + Activities in Class) Assignment 15% Writeen 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 one variables and theory of differential equation. 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 (toanbktp@yahoo.com) • TA: MS. Nguyen Hong Loc
- Faculty of Applied Science - Faculty of Applied Science
Course contents: Chapter 0: Review of Highschool Calculus (One Week) Chapter 1: Function of one variable. Limit and continuity (Two Weeks) Chapter 2: Derivative of function of one variable. Application (Three Weeks) Chapter 3: Integral calculus. Application (Four Weeks) Chapter 4: Differential equation: First order ODE. Application (Two Weeks) Chapter 5: Differential equation: Second order ODE. Application (Two Weeks)
Outcome: After this couse, students are expected to be able to: 1/Evaluate the limil of function of one variable by divers techniques: L’Hospital rule combined with Infinite Smalls – Infinite Greats. 2/ Study the continuity of functions of one variable. 3/ Evaluate derivatives and integral (proper and improper) of function of one variable. 4/ Use derivatives and integral in diverse engineering problems. 5/ Find analytical solution of 1st order ODE for separable, linear and exact cases. 6/ Find analytical solution of 2 nd order ODE in both homogeneous and non – homogeneous cases.
Schedule: Three Class Hours of Lecture + Three Class Hours of Exercise per week
PĐT, Mẫu 2005-ĐC
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Syllabus
PĐT, Mẫu 2005-ĐC
Course Academic Calendar: Week
Content
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Highschool Calculus Review: Solving equations – inequations. Evaluate simple limit. Derivative. Find maximum and minimum. Sketch simple graph. Antiderivative. Definite Integral. Application: Area – Volume. Entry test. Chapter 1: Function of one variable. Limit and continuity 1.1 Catalog of Essential Functions. 1.2 Limit: Simple Definition. Limit Laws. Special Limits 1.3 Indeterminate Forms and L’Hospital’s Rule 1.4 Infinite Smalls and Infinite Greats. 1.5 Continuity Chapter 2: Derivative. Application 2.1 Definition. Derivative & Continuity. One Sided Derivative 2.2 Derivative Laws. 2.3 Implicit Differentiation. 2.4 Derivative of Inverse Trigonometric Functions. 2.5 Derivative of Hyperbolic Functions 2.6 Derivative of Higher Order. 2.7 Linear Approximation and Differential 2.8 Taylor Approximation 2.9 Summary of Curve Sketching Chapter 3: Integral Calculus. Application 3.1 Antiderivative 3.2 New Antiderivative, using Inverse Trigonometric Functions ans Hyperbolic Functions. 3.3 Integration of Rational Functions by Partial Fractions 3.4 Area Problem. The Definite Integral 3.5 The Fundamental Theorem of Calculus 3.6 The Substitution Rule 3.7 Integration by Parts 3.8 Improper integral 3.9 Comparison Test 3.10 Area between curves 3.11 Length 3.12 Volumes Chapter 4: First order ordinary differential equation 4.1 Introduction 4.2 Separable Differential Equation 4.3 Exact Differential Equation. Integration Factor. 4.4 First Order Linear Differential Equation 4.5 Bernulli Differential Equation Chapter 5: Second Order Differential Equation 5.1 Introduction. Reduction Case Chapter 5: Second Order Differential Equation (Continue) 5.2 Second Order Linear Equation with Constant Coefficient: Homogeneous Case 5.3 Nonhomogeneous Case
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Section (in Stewart Book) Lecture
1.1: Pages 24 – 37. 1.2: Pages 88 – 109, Lecture 1.3: Pages 298 – 307 1.4: Lecture 1.5: Pages 119 – 130 2.1: Pages 146, 157 2.2: Pages 183 – 189 2.3: Pages 207 – 212 2.4: Pages 212 – 213 2.5: Pages 254 – 259 2.6: Pages 160 – 161 2.7: Pages 247 – 254 2.8: Lecture 2.9: Pages 307 – 315 3.1: Pages 340 – 342 3.2: Lecture 3.3: Pages 473 – 483 3.4: Pages 355 – 371 3.5: Pages 379 – 387 3.6: Pages 400 – 405 3.7: Pages 453 – 460 3.8: Pages 508 – 514 3.9: Pages 514 – 515 3.10: Pag. 415 – 422 3.11: Pag. 525 – 532 3.12: Pag. 422 – 435 4.1: Pages 569 – 570 4.2: Pages 580 – 591 4.3: Lecture 4.4: Pages 602 – 605 4.5: Lecture Chapter 5: Pages 1111 – 1133 Chapter 5: Pages 1111 – 1133