syllabus mat421 oct 2022

UNIVERSITI TEKNOLOGI MARA
FACULTY OF COMPUTER AND MATHEMATICAL SCIENCES

MAT421 | CALCULUS 1

Lecturer : MDM AMIRAH HANA MOHAMED NOR
Tel (hp) : 0.19-9201003
Email : [email protected]
Office : L2-72
Code : MAT421
Course : Calculus I
Level : Bachelor
Credit Unit :3
Contact Hour :4
Part :1
Course Status : Core
Course Outcomes : At the end of the course, students should be able to:

1. Describe basic concepts and theories related to single-variable calculus.

(C2)

2. Solve problems in single-variable calculus (C3)

3. Demonstrate numeracy skill in tasks related to differentiation and integration

of single- variable calculus. (C3)

Course : This is the first course in calculus series. It starts with topics on functions and
Description
graphs, limits and continuity, techniques of differentiation and integration and its
Syllabus Content
applications.

: 1. Functions, Limits and Continuity

● Functions

● Operations on Functions

● Graph of Functions

● Limits (An Intuitive Introduction and Computational Approach)

● Continuity

● Limits and Continuity of Trigonometric Functions

2. Differentiation
● An Introduction to the Derivative: Tangent
● Definition of Derivative
● Techniques of Differentiation
● Derivatives of Trigonometric, Exponential and Logarithmic Functions
● The Chain Rule
● Implicit Differentiation
● Linear Approximations and Differentials

3. Applications of Differentiation

● Related Rates
● Intervals of Increase and Decrease; Concavity
● First and Second Derivative Tests
● Graphs of Polynomial Functions, Rational Functions; Asymptotes
● Maximum and Minimum Values of a Function
● Applied Maximum and Minimum Problems
● Rolle’s Theorem; Mean-Value Theorem

4. Integration
● Anti-derivatives
● The Indefinite integral
● Integration by Substitution
● Sigma Notation; Area as Limit
● The Definite Integral
● Fundamental Theorems of Calculus
● The Mean Value Theorem for Integrals

Methods of 5. Applications of Integration
Instruction ● Area Between Two Curves
Textbook ● Volumes by Disks and Washer Method
● Volumes by Cylindrical Shell Method
References : Lecture, tutorial, laboratory and discussion will be conducted in the class.

: 1. Stewart,J., Clegg,D., Watson,S.(2021). Calculus: Matric Edition, 9th Edition,
Cengage Learning, 2021, ISBN: 9780357113462

: 1. Anton, H., Bivens,I.C., Davis,S. (2017), Calculus : Early Transcendentals, 11th
Edition, John Wiley & Sons Inc,ISBN: 1119248906.

2. Briggs, W., Cochran, L., Gillet, B., Schulz, E. (2018). Calculus: Single
Variable, 3rd Edition,Pearson Education (US), ISBN: 0134769783

3. Larson, R., Edwards,B.H. (2018). Calculus, 11th Edition, Cengage Learning,
ISBN: 9781337275347.

4. Smith,K.J., Daniele, T.M, Strauss, M.J.(2018). Calculus, 7th Edition, Kendall
Hunt Publishing, ISBN: 1524971359.

5. Neil,H. (2018). Calculus: A Complete Introduction, Illustrated edition, John
Murray Press, ISBN: 1473678447.

Assessment : Final assessment : 50%
● Final Examination Duration: 3 Hours
Continuous assessment
● Quiz : 50%
● Test 20%
● Assignment
20%
10%

SCHEME OF WORK

Week Topics Hours Remark
1 1. 0 FUNCTIONS, LIMITS AND CONTINUITY
1.5
1.1 Functions 1.5
▪ Properties of functions
▪ Domain and range
▪ Operations on functions
▪ Graphs (Family) of functions
Lecture
Discussion

Tutorial/lab 1

1.2 Limits 1.5
▪ Introduction (An intuitive approach) 1.5
1
▪ One-sided limit and two-sided limits
Infinite limits and limits at infinity 1
2 ▪ Computing limits 2
▪ 1

Lecture

Discussion

Tutorial/lab

▪ Computing limits: End behavior

1.3 Continuity

▪ Continuity at a point
3▪ Limits and continuity of trigonometric functions

Lecture

Discussion

Tutorial/lab

1.0 DIFFERENTIATION

2.1 An Introduction to the Derivative: Tangents 1.5
2.2 The Definition of Derivative 1.5
▪ Differentiation from the first principle
▪ Differentiability and continuity 1
4 2.3 Techniques of Differentiation
2.4 Derivatives of Trigonometric, Exponential and Logarithmic Functions
Lecture
Discussion
Tutorial/lab

2.5 The Chain Rule 1.5
2.6 Implicit Differentiation 1.5
2.7 Linear Approximations and Differentials
5 Lecture 1
Discussion
Tutorial/lab

6 3.0 APPLICATIONS OF DIFFERENTIATION 1 QUIZ:
Week 1 1.1-2.7
3.1 Related Rates 1
7 Lecture 1 Remark
Discussion
8 Tutorial/lab Hours
9 QUIZ
1
Topics 2
3.2 Analysis of Functions I: 1
▪ Intervals of increasing and decreasing functions
▪ Concavity and inflection points 1
3.3 Analysis of Functions II: 2
▪ Relative maxima and minima 1
Lecture
Discussion
Tutorial/lab
▪ Critical numbers
▪ First and Second Derivative Test
▪ Graphs of polynomial functions
▪ Graphs of rational functions (linear /linear)
Lecture
Discussion
Tutorial/lab
3.4 Maximum and Minimum Values

▪ Absolute maxima and minima GROUP
3.5 Applied Maximum and Minimum Problems
3.6 Rolle’s Theorem; Mean Value Theorem 1.5 ASSIGNMENT
Lecture 1.5
Discussion 1
Tutorial/lab
10 2
11 4.0 INTEGRATION 1
12 1
Week 4.1 Antiderivatives
4.2 The indefinite integral of algebraic functions and trigonometric TEST:
functions Exponential and Logarithmic Functions 3.1-4.3
4.3 Integration by Substitution
Lecture 1
Discussion 1
Tutorial/lab 1
4.4 Sigma Notation 1
4.5 Area as a limit and the Definite Integrals
▪ Properties of Definite Integrals 1 Remark
Lecture 2
Discussion 1
Tutorial/lab
TEST Hours
4.6 The Fundamental Theorem of Calculus
● The Fundamental Theorem of Calculus, Part 1
● The Fundamental Theorem of Calculus, Part 2
● Evaluating Definite Integrals by Substitution
4.7 The Mean Value Theorem for Integrals
Lecture
Discussion
Tutorial/lab

Topics
5.0 APPLICATIONS OF INTEGRATION

5.1 Area Between Two Curves

13 5.2 Volume: Solids of Revolution 1
● Volume by Disks Method 2
Lecture 1
Discussion
Tutorial/lab 1.5
1.5
5.2 Volume: Solids of Revolution 1
● Volume by Washers Method
5.3 Volume by Cylindrical Shells Method
14 Lecture
Discussion
Tutorial/lab

Assignment

Topics: Functions, Limits and Continuity, Differentiation, and Applications of Differentiation.
A group assignment that requires writing systematic solutions to the calculus problems with the help of
a mathematical software such as MAPLE.
.