Mathematics IA

Course Description

Prerequisites

References

Course Contents

• Chapter 0: Preliminaries
• 0.1 Real Numbers, Estimation, and Logic
• 0.2 Inequalities and Absolute Values
• 0.3 Graphs of Equations
• 0.4 Functions
• 0.5 Trigonometric Functions
• Chapter 1: Limits
• 1.1 Limits Theorem
• 1.2 Limits Involving Trigonometric Functions
• 1.3 Limits at Infinity
• 1.4 Continuity of Functions
• Chapter 2: The Derivative
• 2.1 The Derivative
• 2.2 Derivatives of Trigonometric Functions
• 2.3 The Chain Rule
• 2.4 Higher-Order Derivatives
• 2.5 Implicit Differentiation
• 2.6 Related Rates
• 2.7 Differential and Approximations
• Chapter 3: Applications of the Derivative
• 3.1 Maxima and Minima
• 3.2 Monotomicity and Concavity
• 3.3 Local Extrema and Extrema on Open Intervals
• 3.4 The Mean Value Theorem for Derivatives
• 3.5 Implicit Differentiation
• 3.6 Antiderivatives
• Chapter 4: The Definite Integral
• 4.1 The Definite Integral
• 4.2 The First Fundamental Theorem of Calculus
• 4.3 The Second Fundamental Theorem of Calculus and the Method of Substitution
• 4.4 The Mean Value Theorem for Integrals and the Use of Symmetry
• 4.5 Numerical Integration
• Chapter 5: Applications of the Integral
• 5.1 The Area of a Plan Region
• 5.2 Volume of Solids: Slabs, Disks, Washers
• 5.3 Volume of Solids of Revolution: Shells
• 5.4 Length of a Plane Curve
• 5.5 Work and Fluid Force
• 5.6 Moments and Center of Mass
• 5.7 Probability and Random Variables
• Chapter 6: Transcendental Functions
• 6.1 The Natural Logarithms Function
• 6.2 Inverse Functions and Their Derivatives
• 6.3 The Natural Exponential Function
• 6.4 General Exponential and Logarithmic Functions
• 6.5 Exponential Growth and Decay
• 6.6 First-Order Linear Differential Equations
• 6.7 The Inverse Trigonometric Functions and Their Derivatives
• 6.8 The Hyperbolic Functions and Their Inverses
• Middle Term Exams
• Middle Term Exams
• Final Term Exams
• Final Term Exams