All Courses Math for Machine Learning : Calculus 3
Math for Machine Learning : Calculus 3
Apply multivariable calculus concepts to solve real-world problems. Understand and manipulate vectors and vector-valued functions. Analyze surfaces and volumes using triple integrals. Gain proficiency in partial differentiation and optimization techniques. Interpret and apply the fundamental theorems of vector calculus.
Instructors:
SJ Sushmitha J
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53 Lessons

This course delves into advanced topics of calculus, focusing on functions of multiple variables. Students will explore the concepts of vectors, partial derivatives, multiple integrals, and vector calculus. Emphasis is placed on real-world applications and problem-solving, preparing students for further studies in engineering, physics, computer science, and other fields requiring advanced mathematical skills.

Course Content
Introduction to Vectors
Vector Length and Unit Vectors
Dot Product
The Two Definitions of Dot Product Are Equivalent
Cross Product
Jusification of the Properties of Cross Product
Cross Product and Areas of Parallelograms
More Properties of Cross Product
Equations of Lines and Planes in 3-D Space
More Examples of Lines and Planes in 3D
Parallel and Perpendicular Lines and Planes
Distances between Points, Lines, and Planes
Vector Functions and Space Curves
Closest Point on a Curve
Derivatives and Integrals of Vector Functions
Arclength of Parametric Curves
Functions of Several Variables
Limits of Functions of Several Variables
Proof that sin x is smaller in magnitude than x
Tricky Limit
Partial Derivatives
The Chain Rule for Functions of Several Variables
Justification of the Chain Rule
Directional Derivatives
Tangent Plane
Local Max and Min Values for Functions of Two Variables
The Second Derivatives Test
Proof of the Second Derivatives Test
Lagrange Multipliers
Double Integrals and Riemann Sums
Iterated Integrals
Double Integrals Over General Regions
Double Integrals in Polar Coordinates
Justification of the Area Element when Integrating in Polar Coordinates
The Area under the Normal Curve is 1
Center of Mass
Triple Integrals
Triple Integrals in Cylindrical Coordinates
Spherical Coordinates
Triple Integrals in Spherical Coordinates
Vector Fields
Line Integrals with respect to Arclength
Line Integrals in Terms of Riemann Sums
Line Integrals with Respect to x and y
Line Integrals and Parametrizations
Simple Closed Curves - Definitions
Types of Regions of the Plane - Definitions
Conservative Vector Fields and Independence of Path
Green’s Theorem
Proof of Green’s Theorem
Surface Area of Parametric Surfaces
Divergence
Curl
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