Calculus Of Several Variables
- Sciences
- 300 level
- 3 credit units
- 244 pages
- 23 units
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.
About this course
- Difficulty
- Intermediate
- Study hours
- 150 hours
- Maths
- Advanced
- Content
- Theoretical, problem solving
- Practical work
- No
- Assignments
- Tutor marked assessments
- Final examination
What you'll read
The real module and unit structure of MTH311, taken from the course material NOUN publishes.
One paragraph, so you can see how it reads
MTH311 · UNIT 1 REAL FUNCTION
MAIN CONTENT f is a function from set A to a set B if each element x in A can be associated with a unique element in B. The unique element B which f associates with x in A denoted by f (x).
What you should be able to do
- Calculate limits and determine continuity of multivariable functions
- Compute partial and total derivatives of functions with multiple variables
- Apply chain rule and implicit differentiation techniques
- Expand functions using Taylor's series
- Determine maxima and minima of functions with and without constraints
- Apply Jacobians for coordinate transformations
What it prepares you for
- Data Analyst
- Financial Analyst
- Engineer
- Statistician
- Economist
- Engineering
- Economics
- Physics
- Computer Science
- Finance
Where it gets hard
The units students slow down on, and what makes each one heavy.
- MODULE 3 TOTAL DERIVATIVE OF A FUNCTION.
Unit 2: Total derivative of a function.
Understanding the subtle differences between partial and total derivatives requires careful attention to the dependencies between variables.
- MODULE 5 COMPOSITE DIFFERENTIATION, FULLER'S THEOREM, IMPLICIT DIFFERENTIATION.
Unit 1: Composite differentiation
Applying the chain rule in complex scenarios and understanding the conditions for its validity can be challenging.
- MODULE 7 MAXIMISATION AND MINIMISATION OF FUNCTIONS OF SEVERAL VARIABLES
Unit 2: Lagrange's Multipliers.
Applying Lagrange's multipliers effectively requires a strong understanding of constrained optimization and the ability to solve systems of equations.
A suggested way through it
13 weeks, about 80 hours in total. Yours will differ.
- Week 1Module 1: Limit and Continuity of Functions of Several Variables
Unit 1: Real Functions · 4 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 hours
Understand the concept of limit of a function of several variables. Evaluate limits using different techniques. Solve problems involving limits.
- Week 2Module 1: Limit and Continuity of Functions of Several Variables
Unit 3: Continuity of Function of Several Variables. · 4 hours
Define continuity of a function of several variables. Determine if a function is continuous at a given point. Solve problems involving continuity.
- Week 3Module 2: PARTIAL DERIVATIVES OF FUNCTION OF SEVERAL VARIABLES
Unit 1: Derivative · 4 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 hours
Define partial derivatives of functions of several variables. Compute partial derivatives using different techniques. Understand the geometric interpretation of partial derivatives.
- Week 4Module 2: PARTIAL DERIVATIVES OF FUNCTION OF SEVERAL VARIABLES
Unit 3: Application of Partial derivative. · 4 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 5MODULE 3 TOTAL DERIVATIVE OF A FUNCTION.
Unit 1: Derivation of a function. · 4 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 hours
Define total derivative of a function. Compute total derivatives using different techniques. Understand the relationship between partial and total derivatives.
- Week 6MODULE 3 TOTAL DERIVATIVE OF A FUNCTION.
Unit 3: Application of total derivative of a function. · 4 hours
Apply total derivatives to solve real-world problems. Understand the applications in related fields. Solve problems involving applications of total derivatives.
- Week 7MODULE 4 PARTIAL DIFFERENTIABILITY AND TOTAL DIFFERENTIABILITY OF FUNCTION OF SEVERAL VARIABLE
Unit 1: Partial differentials of function of several variables. · 4 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 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 8MODULE 4 PARTIAL DIFFERENTIABILITY AND TOTAL DIFFERENTIABILITY OF FUNCTION OF SEVERAL VARIABLE
Unit 3:Application of partial and total differentials of function of several variables. · 4 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 9MODULE 5 COMPOSITE DIFFERENTIATION, FULLER'S THEOREM, IMPLICIT DIFFERENTIATION.
Unit 1: Composite differentiation · 4 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 hours
State and apply Fuller's Theorem. Solve problems involving Fuller's Theorem.
- Week 10MODULE 5 COMPOSITE DIFFERENTIATION, FULLER'S THEOREM, IMPLICIT DIFFERENTIATION.
Unit 3: Implicit differentiation. · 4 hours
Understand the concept of implicit differentiation. Apply implicit differentiation to find derivatives. Solve problems involving implicit differentiation.
- Week 11MODULE 6 TAYLOR'S SERIES EXPANSION
Unit 1: Function of two variables · 4 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 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 12MODULE 6 TAYLOR'S SERIES EXPANSION
Unit 3: Application of Taylor's series. · 4 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 13MODULE 7 MAXIMISATION AND MINIMISATION OF FUNCTIONS OF SEVERAL VARIABLES
Unit 1Maximisation and Minimisation Of Functions Of Several Variables. · 4 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 hours
Understand the concept of Lagrange's Multipliers. Apply the definition to solve problems. Solve problems involving Lagrange's Multipliers.
Preparing for the exam
- Thoroughly review all definitions and theorems related to limits, continuity, and differentiability.
- Practice computing partial and total derivatives for a wide range of functions.
- Focus on understanding and applying the chain rule in various contexts.
- Master Taylor's series expansion techniques and their applications.
- Practice solving constrained optimization problems using Lagrange multipliers.
- Review the properties and applications of Jacobians in coordinate transformations.
- Create concept maps linking related topics and formulas for quick recall.
- Work through all examples and tutor-marked assignments to reinforce understanding.
- Allocate sufficient time for practice problems and review of key concepts.
- Form study groups to discuss challenging topics and share problem-solving strategies.
Questions students ask about this course
What is MTH311 about?
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.
How many units does MTH311 have?
MTH311, Calculus Of Several Variables, has 23 units across 8 modules, over 244 pages of course material. You can read it one unit at a time.
How many credit units is MTH311?
MTH311 carries 3 credit units, at 300 level in Sciences.
Is MTH311 hard?
MTH311 is rated intermediate level, with advanced mathematical content. It is mostly theoretical and problem solving work.
How long does MTH311 take to study?
About 150 hours of study, spread across its 23 units.
How is MTH311 assessed?
MTH311 is assessed by assignments, tutor marked assessments and final examination.
What can I do with MTH311?
Data Analyst, Financial Analyst, Engineer, Statistician and Economist.