MA1102R: Calculus
AY2012/2013, Semester 1, Lecturer: Goh Say Song
Course Coverage:
1. Limits
2. Continuous Functions
3. Derivatives
4. Integrals
5. Transcendental Functions
6. Ordinary Differential Equations
This is the introductory module on calculus, one of the most prominent branch of mathematics pioneered by Newton and Leibniz which has a wide range of applications from physics and engineering to business and economics.
The first chapter introduces the fundamental concept of calculus, limits. In particular, this chapter studies how functions behave as it approaches an arbitrary value. Every subsequent topics are then build upon this foundation. The concept of limits to study the properties of functions that are continuous. In layman terms, a continuous function can be drawn in a single stroke.
The concept of limits are further used to develop the most important concepts of calculus, the derivative and integral. The derivative of a function characterizes the behaviour of the function across its domain and the integral is the reverse of this process. The integral of a function is also known as the anti-derivative of the function.
In this course, the concept of continuity, derivative and integrals are further applied to transcendental functions and ordinary differential equations. An important technique of integration through the use of integrating factor, which I unfortunately not remember in the final exam (it comprised a quarter of the paper).
This course is a review of all pre-university mathematics with much higher level of rigour. In pre-university mathematics, the focus has always been applications and computations. However, the focus of this module is more analytical in nature, studying why calculus works instead of how to differentiate and integrate functions. It is a core module for most quantitative majors, and a necessary module for students to understand higher level developments in mathematics. It is also a vital concept in many branches of mathematical applications and modeling.
Workload: Heavy
Difficulty: Moderate
Grade: C+
Course Coverage:
1. Limits
2. Continuous Functions
3. Derivatives
4. Integrals
5. Transcendental Functions
6. Ordinary Differential Equations
This is the introductory module on calculus, one of the most prominent branch of mathematics pioneered by Newton and Leibniz which has a wide range of applications from physics and engineering to business and economics.
The first chapter introduces the fundamental concept of calculus, limits. In particular, this chapter studies how functions behave as it approaches an arbitrary value. Every subsequent topics are then build upon this foundation. The concept of limits to study the properties of functions that are continuous. In layman terms, a continuous function can be drawn in a single stroke.
The concept of limits are further used to develop the most important concepts of calculus, the derivative and integral. The derivative of a function characterizes the behaviour of the function across its domain and the integral is the reverse of this process. The integral of a function is also known as the anti-derivative of the function.
In this course, the concept of continuity, derivative and integrals are further applied to transcendental functions and ordinary differential equations. An important technique of integration through the use of integrating factor, which I unfortunately not remember in the final exam (it comprised a quarter of the paper).
This course is a review of all pre-university mathematics with much higher level of rigour. In pre-university mathematics, the focus has always been applications and computations. However, the focus of this module is more analytical in nature, studying why calculus works instead of how to differentiate and integrate functions. It is a core module for most quantitative majors, and a necessary module for students to understand higher level developments in mathematics. It is also a vital concept in many branches of mathematical applications and modeling.
Workload: Heavy
Difficulty: Moderate
Grade: C+