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Calculus and Linear Algebra (MATH006)
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We have totally 28 classes.
Homework will be assigned after each class.
The average load is three to four questions per section.
Question numbers can be found in this course website.
There will be four quizzes (at week 3, 6, 10, 12).
Homework assignment
Solutions for Midterm Exam
Review of differention: The basic functions and the basic rules
Review of Integration
Solutions for Final Exam
The marks of the final exam will soon be available at the departmental
grading system. If you want to check your own mark and paper, please
come to my office (Room 3453, lift 25/26) in the following time period:
Dec 27 (Wed) 10:00am --- 13:00am
Please note the typos in the answers posted at the course website:
Q5(a): ... -5ln|x|+6^x/ln6...
Q6(c): 12800\pi
Class 1-5: Chapter 4. System of Linear Equations; Matrices
4.1 Review: Systems of Linear Equations in Two Variables
Topics: Systems in two variables, Graphing, Substitution,
Elimination by addition
4.2 Systems of Linear Equations and Augmented Matrices
Topics: Matrices, Solving linear systems using augmented matrices
4.3 Gauss-Jordan Elimination
Topics: Reduced matrices, Solving systems by Gauss-Jordan elimination
4.4 Matrices: Basic Operations
Topics: Addition and subtraction, Product of a number and a matrix,
Matrix product
4.5 Inverse of a Square Matrix
Topics: Identity matrix for multiplication, Inverse of a square matrix
4.6 Matrix Equations and Systems of Linear Equations
Topics: Matrix equations,
Matrix equations and systems of linear equations
Lecture notes for chapter 4
Class 6-7: Chapter 6. Logic, Sets, and Counting
6.2 Sets
Topics: Set properties and set notations, Set operations
6.3 Basic Counting Principles
Topics: Addition principle, Venn diagrams, Multiplication principle
6.4 Permutations and Combinations
Topics: Factorials, Permutations, Combinations
Lecture notes for chapter 6
Class 8-13: Chapter 9. The Derivative
9.1 Introduction to Limits
Topics: Functions and graphs, Limits---A graphical approach,
Limits---An algrebraic approach, Limits of difference quotients
9.2 Continuity
Topics: Continuity, Continuity properties,
Solving inequalities using continuity properties
9.3 The Derivative
Topics: Rate of change, Slope of the tangent line, The derivative,
Nonexistence of the derivative
Lecture notes for chapter 9 (part 1)
9.4 Power Rule and Basic Differentiation Properties
Topics: Constant function rule, Power rule, Constant multiple property,
Sum and difference properties
9.5 Derivatives of Products and Quotients
Topics: Derivatives of products, Derivatives of quotients
9.6 General Power Rule (Chain Rule)
Topics: Chain rule: Power rule, Combining rules of differentiation
Lecture notes for chapter 9 (part 2)
Class 14-15: Chapter 10. Graphing and Optimization
10.1 First Derivative and Graphs
Topics: Increasing and decreasing functions, Local extrema,
First derivative test
10.2 Second Derivative and Graphs
Topics: Concavity, Inflection points, Analyzing graphs,
A graphing strategy for polynomials
10.4 Absolute Maxima and Minima
Topics: Absolute maxima and minima, Second derivative and extrema
Lecture notes for chapter 10
Class 16-20: Chapter 11. Additional Derivative Topics
11.1 The constant e and Continuous Compound Interest
Topics: The constant e, Continuous compound interest
11.2 Exponential Functions and Their Derivatives
Topics: Composite Functions, The Derivative of exp(x),
Graphing techniques for exponential functions
11.3 Logarithmic Functions and Their Derivatives
Topics: Derivative Formulas for ln(x), Other logarithmic and
exponential functions, Graphing techniques
11.4 Chain Rule
Topics: Chain rule
11.5 Implicit Differentiation
Topics: Special function notations, Implicit differentiation
Lecture notes for chapter 11
Class 21-25: Chapter 12. Integration
12.1 Antiderivatives and Indefinite Integrals
Topics: Antiderivatives, Indefinite integrals: Formulas and properties
12.2 Integration by Substitution
Topics: Reversing the chain rule, Integration by substitution,
Additional substitution techniques
12.3 Differential Equations
Topics: Differential equations and slope fields,
Continuous compound interest revisited, Exponential growth law
12.4 The Definite Integral
Topics: Approximating areas by left and right sums,
The definite integral as a limit of sums,
Properties of the definite integral
12.5 The Fundamental Theorem of Calculus
Topics: Evaluating definite integrals,
Recognizing a definite integral:Average value
Lecture notes for chapter 12
Class 26-28: Chapter 13. Additional Integration Topics
13.1 Area Between Curves
Topics: Area between two curves
13.3 Integration By Parts
Topics: The formula for integration by parts
Lecture notes for chapter 13
