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, Comp
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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 f
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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 somethin
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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
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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 tha
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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
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Chapter 7. Matrices, determinants, system of linear equations, eigenvalues and eigenvectors
7.1. Matrix Arithmetic and Operations
This section is devoted to developing the a
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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 varia