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MTH281Sciences3 Unitsintermediate

Mathematical Methods I

This course is designed for undergraduate students in mathematics and physical sciences. It builds upon mathematical concepts from the 100 level, such as differentiation, integration, trigonometric identities, and exponential and logarithmic functions. The course focuses on providing a strong understanding of advanced mathematical methods, including limits, continuity, differentiability, partial differentiation, convergence of infinite series, Taylor and Maclaurin series, and numerical integration techniques. The course is essential for students pursuing careers in mathematics and engineering.

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208h
Study Time
13
Weeks
16h
Per Week
advanced
Math Level
Course Keywords
LimitsDifferentiationSeriesIntegrationMathematical Methods

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

Differentiation

3

Partial Differentiation

4

Infinite Series

5

Taylor and Maclaurin Series

6

Numerical Integration

Total Topics6 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)

graded exercises

Comprehensive evaluation of course material understanding

Written Assessment

tutor-marked assignments

Comprehensive evaluation of course material understanding

Written Assessment

final examination

Comprehensive evaluation of course material understanding

Computer Based Test

Career Opportunities

Explore the career paths this course opens up for you

Mathematician

Apply your skills in this growing field

Engineer

Apply your skills in this growing field

Data Analyst

Apply your skills in this growing field

Statistician

Apply your skills in this growing field

Financial Analyst

Apply your skills in this growing field

Industry Applications

Real-world sectors where you can apply your knowledge

EngineeringFinanceData ScienceResearchAcademia

Study Schedule Beta

A structured 13-week journey through the course content

Week
1

Module 1:

4h

Unit 1: Limit, Continuity and Differentiability

4 study hours
  • •Understand the definition of a limit and how to establish limits of functions.
  • •Learn to determine the continuity of a function and identify points of discontinuity.
  • •Practice differentiation of functions from first principles.
Week
2

Module 1:

4h

Unit 1: Limit, Continuity and Differentiability

4 study hours
  • •Apply Rolle's Theorem and the Mean-Value Theorem to solve problems.
  • •Obtain nth differential coefficients of simple functions using Leibnitz's formula.
  • •Solve problems related to maxima and minima of functions.
Week
3

Module 1:

4h

Unit 2: Partial Differentiation

4 study hours
  • •Understand functions of several independent variables and their properties.
  • •Learn to compute first partial derivatives of functions with respect to different variables.
  • •Apply the chain rule to find partial derivatives of composite functions.
Week
4

Module 1:

4h

Unit 2: Partial Differentiation

4 study hours
  • •Compute higher partial derivatives and verify the commutative property.
  • •Calculate total derivatives and apply them to implicit differentiation.
  • •Solve problems involving homogeneous functions and Euler's Theorem.
Week
5

Module 1:

4h

Unit 2: Partial Differentiation

4 study hours
  • •Apply Lagrange multiplier techniques to find minima and maxima of functions of several variables.
  • •Carry out Taylor series expansion of functions of several variables.
  • •Practice change of variables in partial differential equations.
Week
6

Module 1:

4h

Unit 3: Convergence of Infinite Series

4 study hours
  • •Understand the definition of convergence of infinite series.
  • •Learn and apply theorems related to series convergence.
  • •Test for convergence of series with positive terms using comparison tests.
Week
7

Module 1:

4h

Unit 3: Convergence of Infinite Series

4 study hours
  • •Test for convergence of alternating series.
  • •Distinguish between absolute and conditional convergence.
  • •Apply absolute convergence tests to determine convergence.
Week
8

Module 1:

4h

Unit 3: Convergence of Infinite Series

4 study hours
  • •Understand the concept of power series and their properties.
  • •Perform operations with power series, including multiplication and rearrangement.
  • •Determine the radius and interval of convergence for power series.
Week
9

Module 1:

4h

Unit 4: Taylor and Maclaurin Series

4 study hours
  • •Learn to carry out series expansion using Taylor's and Maclaurin's methods.
  • •Apply Taylor's theorem to expand functions around a specific point.
  • •Apply Maclaurin's theorem to expand functions around zero.
Week
10

Module 1:

4h

Unit 4: Taylor and Maclaurin Series

4 study hours
  • •Evaluate limits of indeterminate forms using Taylor and Maclaurin series.
  • •Apply L'Hopital's rule to evaluate limits.
  • •Solve mathematical problems using Taylor and Maclaurin series expansions.
Week
11

Module 1:

4h

Unit 5: Numerical Integrations

4 study hours
  • •Understand the concept of numerical integration and its applications.
  • •Learn and apply the Trapezium rule for numerical integration.
  • •Apply Simpson's rule for numerical integration.
Week
12

Module 1:

4h

Unit 5: Numerical Integrations

4 study hours
  • •Apply Simpson's rule to solve practical problems.
  • •Use series expansion methods for numerical integration.
  • •Compare and contrast different numerical integration techniques.
Week
13

Module 1:

4h

Unit 5: Numerical Integrations

4 study hours
  • •Review all units and prepare for final examination.
  • •Work on assignments and tutor-marked assignments.
  • •Solve additional problems to reinforce understanding.

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

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Study Tips & Exam Preparation

Expert tips to help you succeed in this course

1

Review all definitions and theorems related to limits, continuity, and differentiability.

2

Practice solving problems involving partial derivatives and their applications.

3

Master the different convergence tests for infinite series and apply them to various series.

4

Understand the derivation and application of Taylor and Maclaurin series.

5

Practice numerical integration techniques, including the Trapezium and Simpson's rules.

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