Course Description:

This course is designed for engineering students who need to acquire skills in calculus as a crash introduction to the mathematics used in engineering. The course emphasizes on the technique of computation without theoretical discussion. Students are expected to have mathematics background equivalent to HKDSE with Extended Module I or II.

Syllabus:

1. Functions

2. Limits

3. Continuity

4. Differentiation

5. Applications of Differentiation

6. Integration

7. Applications of Integration

8. Taylor Series

Assessment:

Coursework (11 sets) There will be 11 sets of coursework in total, the total score will be multiplied by 1.25 (but ceiling at 6%) which becomes the final score of this part of the assessment.	6%
Homework (6 sets) There will be 6 sets of homework in total.	6%
WeBWorK (8 sets) There will be 8 sets of WeBWorK exercises in total.	8%
Midterm Examination (26 Oct)	30%
Final Examination (To be announced. Final exam period: 4 Dec - 20 Dec)	50%

Grade Descriptor:

A

Demonstrates an extensive and detailed knowledge and a deep understanding of the use of Calculus in Engineering; shows highly-developed and perfect arguments for logical deduction; able to provide thoroughly accurate solutions to unfamiliar and nonstandard problems.

A-

Demonstrates a broad knowledge and a strong understanding of the use of Calculus in Engineering; shows almost impeccable consistency in deduction; able to solve some of the unfamiliar and nonstandard problems with high accuracy.

B

Demonstrates an adequate but not complete knowledge and a good understanding of the use of Calculus in Engineering; shows successful derivation with consistency; able to identify and apply appropriate mathematical methods/mathematical operations to solve familiar as well as unfamiliar standard problems.

C

Demonstrates an acceptable knowledge and an understanding, perhaps with gaps, of the use of Calculus in Engineering; shows reasonable but only partially successful attempts in logical deduction; able to solve slight variations of routine problems.

D

Demonstrates a minimum acceptable knowledge and a basic grasp of the use of Calculus in Engineering; presents barely logical and sketchy arguments; able to solve routine problems.

F

Unable to demonstrate sufficient knowledge and understanding of the use of Calculus in Engineering; displays very little knowledge relative to the question posed and in deductive arguments; unable to solve routine problems.

Dr. Hiu Ning CHAN

 LSB 233    3943 7956    hnchan@math.cuhk.edu.hk

 MATH1510A/G  

Dr. Ping Shun CHAN

 LSB 209    3943 7961    pschan@math.cuhk.edu.hk

 MATH1510B/I  

Dr. Man Chuen CHENG

 LSB 210    3943 7985    mccheng@math.cuhk.edu.hk

 MATH1510D/F  

Dr. Kelvin Chun Lung LIU

 LSB 202A    3943 7969    clliu@math.cuhk.edu.hk

 MATH1510E/H  

Dr. Mark Jingjing XIAO

 LSB 210    3943 7985    jjxiao@math.cuhk.edu.hk

 MATH1510C  

References:

Thomas' Calculus / based on the original work by George B. Thomas, Jr. Fifteenth edition in SI Units, Global edition. Harlow : Pearson Education ebook

Calculus, Early Transcendentals / C. Henry Edwards, David E. Penney ebook

Calculus : early transcendentals /James Stewart

Calculus : an applied approach /Ron Larson, Bruce H. Edwards

Calculus with applications for the life sciences /Raymond N. Greenwell, Nathan P. Ritchey, Margaret L. Lial

Calculus : a complete course /Robert A. Adams, Christopher Essex

Calculus /William Briggs, Lyle Cochran

LibrarySearch (Download past papers here) https://julac-cuhk.primo.exlibrisgroup.com/discovery/search?query=any,contains,math1510a&tab=default_tab&search_scope=Exam&vid=852JULAC_CUHK:CUHK&lang=en&offset=0

MathGym (Get help from tutors by making appointment here) http://mathgym.math.cuhk.edu.hk/

E-learning (More reference on pre-calculus and calculus topics) http://www.math.cuhk.edu.hk/~klchan/elearning/index.html

The Myth of Calculus (Role-playing game for learning calculus developed by Dr. Kai Leung CHAN) http://www.math.cuhk.edu.hk/~klchan/www/index.html

Attention is drawn to University policy and regulations on honesty in academic work, and to the disciplinary guidelines and procedures applicable to breaches of such policy and regulations. Details may be found at http://www.cuhk.edu.hk/policy/academichonesty/.

Link to WeBWork: http://webwork.math.cuhk.edu.hk/webwork2

Click HERE for the guideline of using WeBWork

This set of comprehensive notes is written by Dr. Jeff Chak Fu WONG, a former lecturer of this course. Please DO NOT distribute without the author's written permission.

Chapters
Download all HERE
Chapter 1  Vector Alegbra (Same as Note 10-13, Lecture Notes in General Mathematics)
Chapter 2  Functions and their Representations
Chapter 3  The Limit of a Function
Chapter 4  Continuity
Chapter 5  Limits Involving Infinity
Chapter 6  Derivatives and Rate of Changes
Chapter 7  Differentiability
Chapter 8  Derivative of Trigonometric Functions
Chapter 9  Derivative of Exponential Functions & Logarithmic Functions
Chapter 10  Implicit Differentiation
Chapter 11  Polar Coordinates
Chapter 12  Inverse Trigonometric Functions
Chapter 13  Differentials
Chapter 14  Derivatives and Differentials of Higher Orders
Chapter 15  Derivatives and the Shapes of Graphs
Chapter 16  Curve Sketching
Chapter 17  The Mean Value Theorem & Taylor/Maclaurin Series
Chapter 18  Indeterminate Forms and L'Hopital's Rule
Chapter 19  Antiderivatives
Chapter 20  Sigma Notation, Riemann Sums and Distances
Chapter 21  The Definite Integrals
Chapter 22  The Fundamental Theorem of Calculus
Chapter 23  The Substitution Rule
Chapter 24  Integration by Parts
Chapter 25  Trigonometric Integrals and Substitution
Chapter 26  Applications of Integrals: Area between Curves
Chapter 27  Volume of a solid
Chapter 28  Partial Differentiations
Chapter 29  Double Integrals
Chapter 30  Applications of the Fourier Series