FAC1001 — Advanced Mathematics II

Foundation-level Advanced Mathematics II course at Universiti Malaya, Centre for Foundation Studies in Science (PASUM).

Course Description

This course covers advanced mathematical topics including complex numbers, inverse trigonometric functions, and hyperbolic functions. It provides the mathematical foundation for science and computing students.

Topics Covered

Complex Numbers

• Definition and arithmetic of complex numbers
• Polar and exponential forms (Euler's formula)
• De Moivre's theorem
• n-th roots of complex numbers
• Geometric interpretation (circles, perpendicular bisectors, half-lines)
• Complex logarithms and trigonometric functions

Inverse Trigonometric Functions

• Definitions, domains, and ranges
• Principal values and graphs
• Properties and identities
• Derivatives of inverse trig functions
• Applications and evaluations

Hyperbolic Functions

• Definitions in terms of exponentials
• Hyperbolic identities
• Derivatives of hyperbolic functions
• Integrals of hyperbolic functions
• Inverse hyperbolic functions and their logarithmic forms
• Derivatives of inverse hyperbolic functions
• Integrals involving hyperbolic functions

Lecture Sources (11 files)

1. FAC1004 L01 — Complex Numbers
2. FAC1004 L02 — Euler's Formula
3. FAC1004 L5-L6 — Functions of Complex Numbers (n-th Roots)
4. FAC1004 L7-L8 — Complex Equations (Geometric Interpretation)
5. FAC1004 L13 — Inverse Trigonometric Functions
6. FAC1004 L14 — Properties of Inverse Trig Functions
7. FAC1004 L15-L16 — Derivatives of Inverse Trig Functions
8. FAC1004 L17 — Hyperbolic Functions
9. FAC1004 L18 — Hyperbolic Functions (Derivatives & Integrals)
10. FAC1004 L19-L20 — Inverse Hyperbolic Functions
11. FAC1004 L21-L22 — Integrals Involving Hyperbolic Functions

Tutorial Sources (7 files)

1. FAC1004 Tutorial 2 — Complex Numbers
2. FAC1004 Tutorial 3 — Complex Logarithm
3. FAC1004 Tutorial 6 — Inverse Trigonometric Functions
4. FAC1004 Tutorial 7 — Derivatives of Inverse Trig Functions
5. FAC1004 Tutorial 8 — Hyperbolic Functions
6. FAC1004 Tutorial 9 — Inverse Hyperbolic Functions
7. FAC1004 Tutorial 10 — Integration of Hyperbolic Functions

Key Concepts

• Complex Numbers
• Inverse Trigonometric Functions
• Hyperbolic Functions

Related Courses

• FAC1004 - Advanced Mathematics II (Computing) — Computing stream variant
• FAD1014 - Mathematics II — Foundation Mathematics II
• FAD1015 - Mathematics III — Foundation Mathematics III

Institution

Universiti Malaya — PASUM (Program Asasi Sains UM)