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Calculus

Students will learn the core concepts of calculus, including limits, derivatives, integrals, and multivariable calculus. This course provides the mathematical foundation necessary for solving engineering problems involving change, motion, and rates. Students will gain the ability to apply these methods to real-world chemical engineering challenges.


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  • Types of Numbers
  • Linear Equation with Two and Three Variables
  • Inequalities and Absolute Value
  • Domain and Range of Function
  • Cartesian, Cylindrical, and Spherical Coordinate System
  • Algebraic Function
  • Trigonometric Function
  • Composition of Several Function
  • Limit Basic Theorem
  • Limits Involving Polynomial Function
  • Limits Involving Trigonometric Function
  • Limits at Infinity
  • Continuity of Function
  • Application of Limits
  • Basic Concepts of Derivatives
  • Rules for Finding Derivatives
  • The Chain Rule and Leibniz Notation
  • Derivatives for Polynomial Function
  • Derivatives for Trigonometric Function
  • High-Order Derivation
  • Implicite Differentiation
  • Maxima and Minima of Function
  • Monotonicity and Concavity of Function
  • Definite and Indefinite Integral
  • 1st Fundamental Calculus Theorem
  • 2nd Fundamental Calculus Theorem
  • Method of Substitution
  • The Mean Value Theorem for Integral
  • Numerical Integration: Riemann Sum, Trapezoidal Rule, Simpson's Rule
  • The Area of Plane Region
  • Volume of Solids: Slabs, Disks, Washers
  • Volume of Solids of Revolution: Shells
  • Natural Logarithm and Exponential Functions
  • Inverse Function and Their Derivatives
  • General Logarithm and Exponential Functions
  • Exponential Growth and Decay
  • 1st Order Linear Differential Equation
  • Inverse Trigonometric Function and Their Derivatives
  • Hyperbolic Function and Their Inverse

  • Basic Integration Rules
  • Integration by Parts
  • Trigonometric Integrals
  • Rationalizing Substitutions
  • Partial Fraction Method for Integration
  • Strategies for Integration
  • Indeterminate Types of 0/0
  • Other Indeterminate Forms
  • Improper Integrals: Infinite Limits of Integration
  • Improper Integrals: Infinite Integrands
  • Infinite Series and Sequences
  • Positive Series: The Integral Test, Other Tests
  • Alternating Series, Absolute Convergences, and Conditional Convergences
  • Power Series
  • Taylor and MacLaurin Series
  • Taylor Approximation to A Function
  • The Parabola, Ellipses, and Hyperbolas
  • Polar Coordinate System
  • Parametric Function
  • Graphs of Polar Equations
  • Calculus in Polar Coordinates
  • 3D-Cartesian Coordinate System
  • Vector and Scalar
  • Basic Vector Operations: Dot Product, Cross Product
  • Vector-Valued Functions and Curvilinear Motion
  • Lines and Tangent Lines in 3D-System
  • Surfaces in 3D-System
  • Basics Understanding: Function of Two or More Variables
  • Partial Derivatives
  • Limits and Continuity of Function
  • Differentiability
  • Directional Derivatives and Gradients
  • The Chain Rule
  • Tangent Planes and Approximation
  • Maxima and Minima of Function
  • Method of Lagrange
  • Double Integrals over Rectangles, Non-Rectangular Region, and Polar Coordinate
  • Iterated Integrals
  • Triple Integrals in Cartesian, Cylindrical, and Spherical Coordinates
  • Change of Variables in Multiple Integrals

References:

Varberg, D. E., Purcell, E. J., & Rigdon, S. E. (2007). Calculus: Dale Varberg, Edwin J. Purcell, Steven E. Rigdon. Upper Saddle River, N.J: Pearson Prentice Hall.