Calculus and Analytical Geometry
( 25 Modules )

Module #1
Introduction to Calculus
Overview of calculus, its importance, and its applications

Module #2
Limits and Continuity
Definition of limits, properties of limits, and continuity of functions

Module #3
Derivatives
Introduction to derivatives, rules of differentiation, and geometric interpretation

Module #4
Differentiation Rules
Product rule, quotient rule, and chain rule

Module #5
Derivatives of Trigonometric Functions
Derivatives of sine, cosine, and other trigonometric functions

Module #6
Derivatives of Exponential and Logarithmic Functions
Derivatives of exponential and logarithmic functions

Module #7
Implicit Differentiation
Implicit differentiation and its applications

Module #8
Higher-Order Derivatives
Higher-order derivatives and their applications

Module #9
Applications of Derivatives
Optimization problems, motion along a line, and related rates

Module #10
Maxima and Minima
Finding maxima and minima using derivatives

Module #11
Motion Along a Curve
Motion along a curve and related rates

Module #12
Introduction to Integrals
Definition of definite integrals, basic properties, and area under curves

Module #13
Integration Rules
Basic integration rules, substitution method, and integration by parts

Module #14
Integration of Trigonometric Functions
Integration of trigonometric functions and their applications

Module #15
Integration of Exponential and Logarithmic Functions
Integration of exponential and logarithmic functions

Module #16
Applications of Integrals
Area between curves, volume of solids, and surface area

Module #17
Analytical Geometry
Introduction to analytical geometry, equations of lines and planes

Module #18
Curves and Surfaces in Space
Parametric and polar equations of curves and surfaces

Module #19
Vectors in Space
Vectors in space, operations, and applications

Module #20
Vector Calculus
Gradient, divergence, and curl, and their applications

Module #21
Double and Triple Integrals
Double and triple integrals, and their applications

Module #22
Line and Surface Integrals
Line and surface integrals, and their applications

Module #23
Stokes Theorem and Gauss Theorem
Stokes theorem and Gauss theorem, and their applications

Module #24
Greens Theorem and Divergence Theorem
Greens theorem and divergence theorem, and their applications

Module #25
Course Wrap-Up & Conclusion
Planning next steps in Calculus and Analytical Geometry career

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