Contents
2. Limits
2.1. Motivation: Tangent and velocity
2.2. Limit of a function: Using computing device
2.3. Calculating limits with limit laws
2.4. The precise denition of a limit
2.5. Continuity
1
Contents
3. Derivatives
3.1. Derivatives at a point
3.2. The derivative on an interval
3.3. Dierentiation formulas
3.4. Derivatives of trigonometric functions
3.5. Chain rule
3.6. Implicit dierentiati
Contents
4. Further Applications of Integration
4.1. Arc length
4.2. Area of a surface of revolution
4.3. Applications to physics and engineering
1
2
7
10
4. Further Applications of Integration
We hav
Contents
3. Techniques of Integration
3.1. Integration by parts
3.2. Trigonometric integrals
3.3. Trigonometric substitution
3.4. Integration of rational functions by partial fractions
3.5. Strategy f
Contents
2. Applications of Integration
2.1. Areas between curves
2.2. Volumes
2.3. Volumes by cylindrical shells
2.4. Average value of a function
1
2
5
8
10
2. Applications of Integration
This sectio
Contents
Preface
1. Integrals
1.1. Areas and distances
1.2. The denite integral
1.3. The fundamental theorem of calculus
1.4. Indenite integrals and the net change theorem
1.5. The substitution rule
1
MA1301
Solutions
Matrices, Determinants and Systems of Linear Equations
1.
Evaluate
7
2
b
1 1 1
3
1 + a
(a) det 2
(b) det a b c (c) det
4 3
a 1+b
a
b 1+
7
1 3
a 2 b 2 c 2
Solution:
(a)
3 7 2
Contents
0. Preface
1. Functions and Models
1.1. Basic concepts of functions
1.2. Classication of functions
1.3. New functions from old functions
1
2
2
5
9
0. Preface
Instructor:
Prof. Ding-Xuan Zhou,