Calculus
class | topic | Contents of the lecture | professor |
1 | Limits and Continuity | - The Precise Definition of a Limit
- Limits Laws
- Continuity | Prof. Chi-Ok Hwang from GIST |
2 | Derivatives | - Tangents and the Derivative at a Point
- The Derivative as a Function | Prof. Chi-Ok Hwang from GIST |
3 | Applications of Derivatives | - Maximum and Minimum Values
- The Mean Value Theorem | Prof. Chi-Ok Hwang from GIST |
4 | Integral | - Area and Estimating with Finite Sums
- Sigma Notation and Limits of Finite Sums
- The Definite Integral
- Fundamental Theorem of Calculus | Prof. Chi-Ok Hwang from GIST |
5 | Inverse Fuction, Logarithmic Function, and Exponential Function | - The Calculus of Inverse Functions
- Definition of Natural Logarithmic Functions
- Laws of Logarithms
- The Calculus of Natural Logarithmic Functions
- Logarithmic Differentiation
- The Calculus of General Exponential Functions
- The Power Rule
- The Number as a Limit
- Definition of Exponential Function
- Laws of Exponents
- The Calculus of Exponential Function | Prof. Bong-Soo Jang from UNIST |
6 | Inverse Trigonometric and Hyperbolic functions | - Definition of Inverse Trigonometric Function
- Definition of Hyperbolic Function and inverse Hyperbolic - Function
- The Calculus of Inverse Trigonometric and Hyperbolic functions | Prof. Bong-Soo Jang from UNIST |
7 | Volumes | - Definition of Volume
- Solids of Revolution
- Volume of Solids (not revolution) | Prof. Bong-Soo Jang from UNIST |
8 | Volumes by Cylindrical Shells | - Method of Cylindrical Shells | Prof. Bong-Soo Jang from UNIST |
9 | Systems of linear equations | - Matrix representation of system : augmented matrix
- Elementary row operations | Prof. Kang-Jin Han from DGIST |
10 | Systems of linear equations | - Gaussian elimination
- Row echelon form
- Rank of matrix | Prof. Kang-Jin Han from DGIST |
11 | Matrix and Matrix operations | - Matrix Notationphysical variables
- Matrix Operation – addition, multiplication and product of matrix | Prof. Kang-Jin Han from DGIST |
12 | Inverse of matrix | - Invertible matrix
- Inverse matrix
- Left & right inverses | Prof. Kang-Jin Han from DGIST |
13 | Three-Dimensional Coordinate Systems Vectors | - Distance Formula in Three Dimensions
- Equation of a Sphere
- Vector Addition
- Scalar mutiplication
- Properties of Vectors | Prof. Hyung-Ryul Baik from KAIST |
14 | The Dot Product | - Dot Product
- Properties of the Dot Product
- Direction Angles and Direction Cosines
- Projections | Prof. Hyung-Ryul Baik from KAIST |
15 | The Cross Product | - Cross Product
- Triple Products | Prof. Hyung-Ryul Baik from KAIST |
16 | Equations of Lines and Planes | - Vector equation
- Parametric equations
- Planes | Prof. Hyung-Ryul Baik from KAIST |
