Login Create Account

Back to Course Catalog

MTH311Sciences3 Unitsintermediate

Calculus Of Several Variables

This course introduces students to the calculus of several variables. It covers topics such as limits and continuity of functions of several variables, partial derivatives, total derivatives, partial and total differentiability, composite differentiation, Taylor's series expansion, maximisation and minimisation, and Jacobians. The course aims to provide a solid foundation for further studies in mathematical analysis and its applications.

Generate AI Study Notes

Transform this course into personalized study materials with AI

150h

Study Time

13

Weeks

12h

Per Week

advanced

Math Level

Course Keywords

CalculusMultivariable FunctionsPartial DerivativesTotal DerivativesJacobians

Course Overview

Everything you need to know about this course

Course Difficulty

Intermediate Level

Builds on foundational knowledge

65%

intermediate

∑

Math Level

Advanced Math

📖

Learning Type

Theoretical Focus

Course Topics

Key areas covered in this course

1

Limits and Continuity

2

Partial Derivatives

3

Total Derivatives

4

Partial and Total Differentiability

5

Composite Differentiation

6

Taylor's Series Expansion

7

Maximisation and Minimisation

8

Jacobians

Total Topics8 topics

Ready to Start

No specific requirements needed

This course is designed to be accessible to all students. You can start immediately without any prior knowledge or specific preparation.

Assessment Methods

How your progress will be evaluated (3 methods)

assignments

Comprehensive evaluation of course material understanding

Written Assessment

tutor-marked assessments

Comprehensive evaluation of course material understanding

Written Assessment

final examination

Comprehensive evaluation of course material understanding

Written Assessment

Career Opportunities

Explore the career paths this course opens up for you

Data Analyst

Apply your skills in this growing field

Financial Analyst

Apply your skills in this growing field

Engineer

Apply your skills in this growing field

Statistician

Apply your skills in this growing field

Economist

Apply your skills in this growing field

Industry Applications

Real-world sectors where you can apply your knowledge

EngineeringEconomicsPhysicsComputer ScienceFinance

Study Schedule Beta

A structured 13-week journey through the course content

Week

1

Module 1: Limit and Continuity of Functions of Several Variables

8h

Unit 1: Real Functions

4 study hours

•Define real-valued functions and their domains
•Identify different types of functions and their graphs
•Solve problems involving function values

Unit 2: Limit of Function of Several Variables.

4 study hours

•Understand the concept of limit of a function of several variables
•Evaluate limits using different techniques
•Solve problems involving limits

Week

2

Module 1: Limit and Continuity of Functions of Several Variables

4h

Unit 3: Continuity of Function of Several Variables.

4 study hours

•Define continuity of a function of several variables
•Determine if a function is continuous at a given point
•Solve problems involving continuity

Week

3

Module 2: PARTIAL DERIVATIVES OF FUNCTION OF SEVERAL VARIABLES

8h

Unit 1: Derivative

4 study hours

•Understand the concept of derivative
•Apply the definition to find the derivative of simple functions
•Solve problems involving derivatives

Unit 2: Partial derivative.

4 study hours

•Define partial derivatives of functions of several variables
•Compute partial derivatives using different techniques
•Understand the geometric interpretation of partial derivatives

Week

4

Module 2: PARTIAL DERIVATIVES OF FUNCTION OF SEVERAL VARIABLES

4h

Unit 3: Application of Partial derivative.

4 study hours

•Apply partial derivatives to solve real-world problems
•Understand the applications in optimization and related fields
•Solve problems involving applications of partial derivatives

Week

5

MODULE 3 TOTAL DERIVATIVE OF A FUNCTION.

8h

Unit 1: Derivation of a function.

4 study hours

•Understand the concept of derivation of a function
•Apply the definition to derive simple functions
•Solve problems involving derivation of a function

Unit 2: Total derivative of a function.

4 study hours

•Define total derivative of a function
•Compute total derivatives using different techniques
•Understand the relationship between partial and total derivatives

Week

6

MODULE 3 TOTAL DERIVATIVE OF A FUNCTION.

4h

Unit 3: Application of total derivative of a function.

4 study hours

•Apply total derivatives to solve real-world problems
•Understand the applications in related fields
•Solve problems involving applications of total derivatives

Week

7

MODULE 4 PARTIAL DIFFERENTIABILITY AND TOTAL DIFFERENTIABILITY OF FUNCTION OF SEVERAL VARIABLE

8h

Unit 1: Partial differentials of function of several variables.

4 study hours

•Define partial differentials of functions of several variables
•Compute partial differentials using different techniques
•Understand the relationship between partial derivatives and partial differentials

Unit 2: Total differentials of function of several variables.

4 study hours

•Define total differentials of functions of several variables
•Compute total differentials using different techniques
•Understand the relationship between total derivatives and total differentials

Week

8

MODULE 4 PARTIAL DIFFERENTIABILITY AND TOTAL DIFFERENTIABILITY OF FUNCTION OF SEVERAL VARIABLE

4h

Unit 3:Application of partial and total differentials of function of several variables.

4 study hours

•Apply partial and total differentials to solve real-world problems
•Understand the applications in related fields
•Solve problems involving applications of partial and total differentials

Week

9

MODULE 5 COMPOSITE DIFFERENTIATION, FULLER'S THEOREM, IMPLICIT DIFFERENTIATION.

8h

Unit 1: Composite differentiation

4 study hours

•Understand the concept of composite differentiation
•Apply the chain rule to differentiate composite functions
•Solve problems involving composite differentiation

Unit 2: Fuller's Theorem

4 study hours

•State and apply Fuller's Theorem
•Solve problems involving Fuller's Theorem

Week

10

MODULE 5 COMPOSITE DIFFERENTIATION, FULLER'S THEOREM, IMPLICIT DIFFERENTIATION.

4h

Unit 3: Implicit differentiation.

4 study hours

•Understand the concept of implicit differentiation
•Apply implicit differentiation to find derivatives
•Solve problems involving implicit differentiation

Week

11

MODULE 6 TAYLOR'S SERIES EXPANSION

8h

Unit 1: Function of two variables

4 study hours

•Understand the concept of function of two variables
•Apply the definition to solve problems
•Solve problems involving function of two variables

Unit 2: Taylor's series expansion for functions of two variables.

4 study hours

•Understand the concept of Taylor's series expansion for functions of two variables
•Apply the definition to solve problems
•Solve problems involving Taylor's series expansion for functions of two variables

Week

12

MODULE 6 TAYLOR'S SERIES EXPANSION

4h

Unit 3: Application of Taylor's series.

4 study hours

•Apply Taylor's series to solve real-world problems
•Understand the applications in related fields
•Solve problems involving applications of Taylor's series

Week

13

MODULE 7 MAXIMISATION AND MINIMISATION OF FUNCTIONS OF SEVERAL VARIABLES

8h

Unit 1Maximisation and Minimisation Of Functions Of Several Variables.

4 study hours

•Understand the concept of maximisation and minimisation of functions of several variables
•Apply the definition to solve problems
•Solve problems involving maximisation and minimisation of functions of several variables

Unit 2: Lagrange's Multipliers.

4 study hours

•Understand the concept of Lagrange's Multipliers
•Apply the definition to solve problems
•Solve problems involving Lagrange's Multipliers

This study schedule is in beta and may not be accurate. Please use it as a guide and consult the course outline for the most accurate information.

Course PDF Material

Read the complete course material as provided by NOUN.

Access PDF Material

Study Tips & Exam Preparation

Expert tips to help you succeed in this course

1

Thoroughly review all definitions and theorems related to limits, continuity, and differentiability.

2

Practice computing partial and total derivatives for a wide range of functions.

3

Focus on understanding and applying the chain rule in various contexts.

4

Master Taylor's series expansion techniques and their applications.

5

Practice solving constrained optimization problems using Lagrange multipliers.

6

Review the properties and applications of Jacobians in coordinate transformations.

7

Create concept maps linking related topics and formulas for quick recall.

8

Work through all examples and tutor-marked assignments to reinforce understanding.

9

Allocate sufficient time for practice problems and review of key concepts.

10

Form study groups to discuss challenging topics and share problem-solving strategies.

Related Courses

Other courses in Sciences that complement your learning

Noise And Air Pollution

Electronics Ii

Mathematical Methods Iii

View All Sciences Courses