Math1013 Calculus I

Course Outline- Spring 2012-13

1.      Instructor(s)

Name: Prof. Edmund Y. M. Chiang

Contact Details:  Office: Room 3488        Phone: 2358-7441       Email:machiang@ust.hk

       Office hours: Every Monday from 16:00 to 17:00.

 

2.      Teaching Assistant

Name: Mr. Henry K. M. Cheng (kero@ust.hk) Tutorial notes

 

3.      Meeting Time and Venue

Lectures:

Date/Time/Venue: L1 : Monday and Wednesday : 12:00 – 13:20 / Room 2464

　

Tutorials:

Date/Time/Venue: Friday  T1A in room 4333 (Lift 3; 18:00-18:50), T1B in room 4333 (Lift 3; 19:00-19:50)

 

4.      Course Description

Credit Points:          3

Pre-requisite:           NIL

Exclusion:   AL Pure Mathematics; AL Applied Mathematics; MATH 1003, MATH 1018, MATH 1020,

MATH 1023, MATH 1024; any MATH course at or above 100-/2000- level

Brief Information/synopsis:

This is an introductory course in one-variable calculus. Topics include functions and their limits, continuity, derivatives and rules of differentiation, applications of derivatives, and basic integral calculus. (For other related courses offered by the Math Dept, please refer to the web site: http://www.math.ust.hk/ug/intranet/calculus.shtml

Intended Learning Outcomes

Upon successful completion of this course, students should be able to:

No.

ILOs

1

express quantitative relationships using the language of functions

2

develop basic computational skills in calculus

3

apply the concepts and methods of calculus in modeling and problem solving

 

5.      Assessment Scheme

Assessment

Assessing Course ILOs

9% by homework and 6% on 3 WeBWork

3% by quizzes (3 WeBWork; 2 before, 1 after midtem)

1, 2, 3

1, 2, 3

30% by midterm exam

1, 2, 3

55% by final exam

1, 2, 3

  • Tentative schedule of homework will be due on 11 Mar., 25 Mar., 22nd Apr., 8/13 May. Homework support will be given in the tutorials. Homework 1

  • online via the webwork platform.

  • Mid-semester examination date: 8th (Mon) April 2013 at 19:30-21:00.

　

　

6.      Student Learning Resources

Text:

W. Briggs, L. Cochran, and B. Gillett, “Calculus for Scientists and Engineers – Early Transcendentals”, Pearson.

Weekly worksheets: TBD

Presentation notes: Chapter 1, Trigonometry, Limits (revised), Derivative , Derivative II, Derivative III, Derivative IV, Integration I, Integration II,  Revision

Lecture notes for Mathematical Analysis: Chapters I, II, III, IV, V, VI, VII, VIII (Comments: These notes are NOT part of this course. It is for those students who are interested to know more about the "epsilon-delta" type mathematical analysis. The chapters on limits of functions, continuity, differentiations and integrations are most relevant).

 

7.      Teaching and Learning Activities

            Scheduled activities: 4 hrs (lecture + tutorial)

  • Weekly office hour: Monday: 16:00-17:00

  • Math Support Centre:      Library Learning Commons, Classroom: time and venue

Extra (ungraded) exercises from the textbook

 

8.      Course Schedule

Keyword Syllabus:

Functions and limits, continuity, derivatives, anti-derivatives, definite integrals and the Fundamental Theorem of Calculus.

           

      Weekly Schedule:

 

            Week one: Monday (Feb. 4):

Functions, their graphs, and compositions. (1.1)

Representing functions. (1.2)

Inverse functions, exponential and logarithm. (1.3)

 

Week two (Feb. 11th Feb: Chinese New Year)  No lectures

　

Week three: Monday (Feb 18):

Trigonometric functions and their inverses. (1.4)

The idea of limits. (2.1)

Definition of limit. (2.2)

 

Week four: Monday (Feb 25):

Computations of limits, infinite limits. (2.3, 2.4)

Limits at infinity. (2.5)

Continuity, intermediate value theorem. (2.6)

 

Week five: Wednesday (Mar 04): 

Derivatives. (3.1)

Differentiation rules (3.2)

 

Week six: Monday (Mar 11):

Differentiation rules, product, quotient. (3.2, 3.3)

Derivatives of trigonometric functions. (3.4)

Derivative as rate of change. (3.5)

Chain rule. (3.6)

 

Week seven: Monday (Mar. 18):

Implicit differentiation. (3.7)

Derivatives of exponential and logarithmic functions. (3.8)

Derivatives of inverse trigonometric functions. (3.9)

 

Week eight: Monday (Mar. 25):

Related Rates. (3.10)

Applications, maxima, minima. (4.1)

 

Week nine: Monday (Apr. 8) :

Uses of derivative, graphing. (4.2, 4.3)

Optimization problems. (4.4)

 

Week ten: Monday (Apr. 15):

Linear approximations. (4.5)

Mean value theorem. (4.6)

L'Hopital's rule. (4.7)

 

Week eleven: Monday (Apr. 22):

Newton's method (4.8)*

Anti-derivatives. (4.9)

 

Week twelve: Monday (Apr 29) (Holiday 1 May):

Approximating areas under curves. (5.1)

Definite integrals. (5.2)

 

Week thirteen: Monday (May 6):

The Fundamental Theorem of Calculus. (5.3)

Applications. (5.4)

 

Week fourteen: Monday (Dec 13): .

Substitution. (5.5)

.