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Mathematical Foundations (II)
👨🏫 Welcome
🖊️ Homework
🤔 Q and A
📖 Course Outline
I 💡 LECTURE NOTES
Revision and Warm-up
Exponents
Algebraic Identities and Algebraic Expressions
Solving Linear Equations
Solving Quadratic Equations
Remainder Theorem and Factor Theorem
Solving Linear Inequalities
Lines
Pythagoras Theorem, Distance Formula and Circles
Parabola
Systems of Equations
1
Sets, Real Numbers and Inequalities
1.1
Sets
1.1.1
Introduction
1.1.2
Set operations
1.2
Real Numbers
1.2.1
The Number Systems
1.2.2
Radicals
1.3
Solving Inequalities
2
More Functions and Graphs
2.1
Functions
2.2
Domains and Ranges
2.3
Graphs of Equations
2.4
Graphs of Functions
2.5
Compositions of Functions
2.6
Inverse Functions
2.7
More on Solving Equations
3
Limits
3.1
Introduction
3.2
Limits of Sequences
3.3
Limits of Functions at Infinity
3.4
One-sided Limits
3.5
Two-sided Limits
3.6
Continunous Functions
4
Trigonometric Functions
4.1
Angles
4.2
Trigonometric Functions
4.3
Differentiation of Trigonometric Functions
5
More Integration
5.1
More Formulas
5.2
Subsitution Method
5.3
Integration of Rational Functions
5.4
Integration by Parts
5.5
More Applications of Definite Integrals
6
Vectors and Geometry of Space
6.1
Three-Dimensinal Coordinate Systems
6.2
Vectors
6.3
Dot Product
6.4
Cross product
6.5
Equations of Lines and Planes
6.6
Directional Derivatives and Gradient Vector
7
Matrices
7.1
Basic Matrix Operations
7.2
Matrix Inversion
7.3
Cramer’s rule
II 💡 SOLUTIONS
Chapter 1
Exercise 1.1
Q1
Q2
Exercise 1.2
Q1
Q2
Exercise 1.3
Q1
Q2
Q3
Chapter 2
Exercise 2.1
Exercise 2.2
Q1
Q2
Exercise 2.3
Q1
Q2
Q3
Q4
Q5
Exercise 2.4
Q4
Q5
Exercise 2.5
Q2
Exercise 2.6
Q2
Exercise 2.7
Q1
Q2
Q3
Q4
Chapter 3
Exercise 3.1
Q1
Exercise 3.2
Q1
Q2
Q3
Exercise 3.3
Q1
Q3
Q4
Exercise 3.4
Q1
Exercise 3.5
Q1
Exercise 3.6
Q1
Q2
Q3
Q4
Q5
Chapter 4
Exercise 7.1
Q1
Q2
Exercise 7.2
Q1
Q2
Exercise 7.3
Q1
Q2
Q3
Q4
Chapter 5 More on integration
Exercise 10.1
Q1
Q2
Q3
Exercise 10.2
Q1
Q2
Q3
Exercise 10.3
Q1
Q2
Q3
Solutions to Exercise 10.3
Q1
Q2
Q3
Exercise 10.4
Q1
Q2
Q3
Solutions to Exercise 10.4
Q1
Q2
7.3.1
Exercise 10.5
Q1
Q2
Q3
Solutions to Exercise 10.5
Q1
Q2
Q3
Chapter 6 Vectors
Exercise 6.1
Q1
Q2
Q3
Q4
Solutions to Exercise 6.1
Q1
Q2
Q3
Q4
GitHub repo
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Mathematical Foundations (II)
7
Matrices
7.1
Basic Matrix Operations
7.2
Matrix Inversion
7.3
Cramer’s rule