Calculus
Topic outline

Synopsis
Calculus is the mathematics of change, calculating problems that are continually evolving. This is possible by breaking such problems into infinitesmall steps, solving each of those steps, and adding all results. Rather than doing each step individually, calculus allows these computations to be done simultaneously. There are two primary branches of calculus: differential and integral. Therefore, students are exposes to limits and continuity, differentiation, application of differentiation, integration, and application of integration. This course integrates symbolic tools, graphical concepts and numerical calculations.
Content
Course Outcomes
By the end of this course, student should be able to
(i) Acquire and apply the fundamental principle of calculus
(ii) Apply the appropriate method to solve mathematical problems
(iii) Provide solution to solve mathematical problems arise from real life
References
1. Abdul Wahid Md Raji, Hamisan Rahmat, Ismail Kamis, Mohd Nor Mohamad, Ong Chee Tiong. The First Course of Calculus for Science & Engineering Students, Second Edition, UTM 2016.
2. Siti Zanariah Satari, Mohd Nizam Kahar, Norazaliza Mohd Jamil, Calculus for Science & Engineering, First Edition, UMP 2010.
3. Norazaliza Mohd Jamil, Nor Alisa Mohd Damanhuri, Yuhani Yusof, Nor Aida Zuraimi Md Noar, Norhafizah Md Sarif, Mathematical Formulae, First Edition, UMP 2017.

Forum


Chapter 1A : Limit & Continuity
1.1 Limit of a Function
1.2 Evaluating Limit
1.2.1 Evaluate Limit using Numerical Method
1.2.2 Evaluate Limit using Graphical Method
1.2.3 Evaluate Limit using Analytical Method 
Chapter 1B : Limit & Continuity
2.1 Limit at a Infinity
2.2 Continuity

Chapter 2A : Differentiation
3.1 Introduction to Differentiation
3.2 Derivative of a Functions
3.3 Techniques of Differentiation

Chapter 2B : Differentiation
4.1 Implicit Differentiation
4.2 Parametric Equation
4.3 Higher Derivative

Chapter 3A : Applications of Differentiation
5.1 Curve Slope at a Point
5.2 Rate of Change

Chapter 3B : Applications of Differentiation
6.1 First Derivative Test
6.2 Second Derivative Test
6.3 Inflection Points

Chapter 4A : Integrations
7.1 Antiderivatives
7.2 Indefinite Integrals
7.3 Definite Integrals

Chapter 4B : Integrations
8.1 Integration by Substitution
8.2 Integration by Parts
8.3 Integration using Partial Fractions

Chapter 5A : Applications of Integration
9.1 Area
9.1.1 Area Under a Curve
9.1.2 Area Between Two Curves9.2 Surface Area

Chapter 5B : Applications of Integration
10.1 Volume  Slicing Method
10.2 Volume  Disk Method
10.3 Volume  Cylindrical Shells

Past Year Final Examination Questions
