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Calculus Lecture Videos
Limits and Continuity
Intuitive definition of limits
limit laws and elementary methods
sandwich theorem and a famous limit related to trigonometric functions
Definition of Limits at Infinity
continuity and discontinuous points
properties of continuous functions and intermediate value theorem
formal (precise) definition of a limit
Derivatives
Definition of Derivatives
Basic formula of derivatives
differentiation rules
Chain rule for composition functions
Implicit Differentiation
logarithm differentiation
Derivative of Inverse Functions
Derivative of I inverse Trigonometric Functions
Higher Order Derivatives
Related Rates
Calculus Methods and Skills
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Linear Systems
Linear Systems
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Ho to Solve Linear System
How to Determine if a Linear System is Consistent or Inconsistent?
How to Determine if a Vector Set is Linearly Dependent or Independent?
Linear Transformation and Its Stand Matrix
How to Compute Inverse Matrix?
How to Find Null Space and Column Space of a Matrix?
How to Evaluate Determinant?
Methods and Skills
Multivariable Calculus Lecture Videos
Vectors and Analytic Geometry
Concepts of Vectors
Linear Operations of Vectors
Three Dimensional Coordinates
Projection, Direction Angle and Direction Cosine
Dot Product
Cross Product
Triple Scalar Product
Equation of Lines
Equations of Planes
Distance from a Point to a Line or to a Plane
Distance Between Lines or Between Planes
Equations of Cylinders and Surfaces of Revolution
Quadric Surfaces
Space Curves
Partial Derivatives and Their Applications
Functions of Several Variables
Limit and Continuity of Several Variable Functions
Partial Derivatives
Higher Partial Derivatives
Proof of Clairaut’s Theorem Equqlity of Mixed Derivative
Differentiability and Total Differential
Chain Rule for Multivariable Functions
Implicit Differential for Multivariable Functions
Directional Derivatives
Gradient Vector
Tangent Planes and Normal Lines
Maximum and Minimum of Multivariable Functions
Lagrange Multiplier
Lagrange Multiplier with Two Constraints
Multiple Integration
Definition of Multiple Integrals
How to Evaluate Double Integrals in Rectangular Coordinates
More Examples of Double Integrals in Rectangular Coordinates
Properties of Double Integrals
Polar Coordinates
Evaluate Double Integrals in Polar Coordinates
Evaluate Surface Area Using Double Integrals
Evaluate Surface Area for Parametric Surfaces
Triple Integrals in Rectangular Coordinates
Evaluate Triple Integrals in Cylindrical Coordinates
Evaluate Triple Integrals in Spherical Coordinates
Multivariable Calculus Methods and SKills
Review and Summary
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Vector Calculus Lecture Videos
Vector Valued Functions and Space Curves
Vector Valued Functions and Parametric Curves
Arc Length and Reparametrized by Arc Length
Curvature and Unit Normal Vector
Binormal, Torsion and Frenet’s Formula
Curvature and Torsion for General Parametrizations
Line Integrals
Line Integrals of Arc Length
Vector Fields and Conservative Vector Fields
Line Integrals of Vector Fields
Green’s Theorem
Evaluate Line Integrals Using Green’s Theorem
Finding the Area Using Green’s Thoerm
Fundamental Theorem of Line Integrals
Independence of Path
Surface Integrals
Fundamental Theorem of Line Integrals
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How to Find the Standard Matrix of a Linear Transformation?
How to Determine the Type of Discontinuous Points?
What are Common Methods to Evaluate Limits?
How to Determine if a Vector Set is Linearly Dependent or Independent?
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