MATH1804 University Mathematics A
Dr. Yat-Ming Chan
Department of Mathematics The University of Hong Kong
First Semester 2009-10
Content Outline 1. Pre-Calculus Topics Sets, Functions and Graphs, Composite and Inverse Functions, Limits and Continuity. 2.
Ch2/MATH1804/YMC/2009-10
1
Chapter 2. Functions
2.1. Functions and Graphs
The idea of a function expresses the dependence between two quantities, one of which is given and the other is the output. A function associates a unique output with every input ele
Ch3/MATH1804/YMC/2009-10
1
Chapter 3. Limits and Continuity
3.1. Limits
The concept of a limit lies at the foundation of calculus. The idea involves the notion of getting closer and closer to something, but yet not touching it. Limits are used to dene con
Ch4/MATH1804/YMC/2009-10
1
Chapter 4. Dierentiation and Its Applications
4.1. Review of derivatives
Dierence quotient and Derivatives The dierence quotient of a function f (x) at x = a with increment h is given by f (a + h) f (a) h and the derivative of
Ch5/MATH1804/YMC/2009-10
1
Chapter 5. Exponential and Logarithmic Functions
5.1. Review
Exponential Functions An exponential function is a function of the form f (x) = ax where a > 0, a = 1. Note that the exponent x can be any real number here, and the n
Ch6/MATH1804/YMC/2009-10
1
Chapter 6. Integration
6.1. The Fundamental Theorem of Calculus
The principal theorem of this section is the Fundamental Theorem of Calculus, which is the central theorem of integral calculus. It provides a connection between th
Ch7/MATH1804/YMC/2009-10
1
Chapter 7. Matrices, determinants, system of linear equations, eigenvalues and eigenvectors
7.1. Matrix Arithmetic and Operations
This section is devoted to developing the arithmetic of matrices. We will see some of the dierence
Ch8/MATH1804/YMC/2009-10
1
Chapter 8. Partial Dierentiation
Many functions depend on more than one variable. It is then natural to extend the basic ideas of the calculus of functions of a single variable to functions of several variables. Let us rst study