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MTH341Sciences3 Unitsintermediate

Real Analysis

This course introduces students to the fundamental concepts of real analysis, focusing on differentiability and mean value theorems. It covers derivatives, their geometrical interpretation, and the relationship between continuity and differentiability. Students will explore Rolle's theorem, Lagrange's mean value theorem, and Cauchy's mean value theorem. The course also delves into higher order derivatives, Taylor's theorem, Maclaurin's expansion, indeterminate forms, and extreme values of functions.

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208h
Study Time
13
Weeks
16h
Per Week
advanced
Math Level
Course Keywords
Real AnalysisDifferentiabilityMean Value TheoremsTaylor's TheoremIndeterminate Forms

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

Derivatives

2

Mean Value Theorems

3

Rolle's Theorem

4

Lagrange's Theorem

5

Cauchy's Theorem

6

Taylor's Theorem

7

Maclaurin's Expansion

8

Indeterminate Forms

9

L'Hospital's Rule

10

Extreme Values

Total Topics10 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 assignments

Comprehensive evaluation of course material understanding

Written Assessment

final examination

Comprehensive evaluation of course material understanding

Written Assessment

Career Opportunities

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Data Analyst

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Financial Analyst

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Statistician

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Research Scientist

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Mathematician

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Industry Applications

Real-world sectors where you can apply your knowledge

FinanceEngineeringData ScienceResearchAcademia

Study Schedule Beta

A structured 13-week journey through the course content

Week
1

Module 1: Differentiability

4h

Unit 1: Derivatives

4 study hours
  • •Understand the definition of the derivative of a function at a point.
  • •Explore the geometrical interpretation of the derivative as the slope of a tangent.
  • •Study the relationship between differentiability and continuity.
Week
2

Module 1: Differentiability

4h

Unit 2: Mean-Value Theorems

4 study hours
  • •Learn and apply Rolle's Theorem to solve problems.
  • •Understand and apply Lagrange's Mean Value Theorem.
  • •Explore Cauchy's Mean Value Theorem and its applications.
Week
3

Module 1: Differentiability

4h

Unit 3: Higher Order Derivatives

4 study hours
  • •Study higher order derivatives and their properties.
  • •Learn Taylor's Theorem and Maclaurin's Expansion.
  • •Practice finding derivatives of various functions.
Week
4

Module 1: Differentiability

4h

Unit 1: Derivatives

4 study hours
  • •Review derivatives of a function
  • •Practice problems on geometrical meaning of derivatives
  • •Work on tutor marked assignment
Week
5

Module 1: Differentiability

4h

Unit 2: Mean-Value Theorems

4 study hours
  • •Review Rolle's Theorem
  • •Practice problems on Lagrange's Mean Value Theorem
  • •Work on tutor marked assignment
Week
6

Module 1: Differentiability

4h

Unit 3: Higher Order Derivatives

4 study hours
  • •Review Taylor's Theorem
  • •Practice problems on Maclaurin's Expansion
  • •Work on tutor marked assignment
Week
7

Module 1: Differentiability

4h

Unit 1: Derivatives

4 study hours
  • •Solve problems involving limits using L'Hopital's rule.
  • •Practice converting indeterminate forms to apply L'Hopital's rule.
  • •Review various indeterminate forms and their evaluation techniques.
Week
8

Module 1: Differentiability

4h

Unit 2: Mean-Value Theorems

4 study hours
  • •Apply first and second derivative tests to find local maxima and minima.
  • •Solve optimization problems using calculus techniques.
  • •Review conditions for local and global extrema.
Week
9

Module 1: Differentiability

4h

Unit 3: Higher Order Derivatives

4 study hours
  • •Review derivatives of a function
  • •Practice problems on geometrical meaning of derivatives
  • •Work on tutor marked assignment
Week
10

Module 1: Differentiability

4h

Unit 1: Derivatives

4 study hours
  • •Solve problems involving limits using L'Hopital's rule.
  • •Practice converting indeterminate forms to apply L'Hopital's rule.
  • •Work on tutor marked assignment
Week
11

Module 1: Differentiability

4h

Unit 2: Mean-Value Theorems

4 study hours
  • •Apply first and second derivative tests to find local maxima and minima.
  • •Solve optimization problems using calculus techniques.
  • •Work on tutor marked assignment
Week
12

Module 1: Differentiability

4h

Unit 3: Higher Order Derivatives

4 study hours
  • •Review all units
  • •Practice problems on all topics
  • •Prepare for final examination
Week
13

Module 1: Differentiability

4h

Unit 3: Higher Order Derivatives

4 study hours
  • •Final Revision
  • •Work on pending assignments
  • •Prepare for final examination

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

Thoroughly review the definitions and theorems covered in each unit.

2

Practice solving a variety of problems related to derivatives and mean value theorems.

3

Focus on understanding the conditions required for applying each theorem.

4

Create concept maps linking Taylor's and Maclaurin's theorems to specific function expansions.

5

Practice applying L'Hospital's Rule to different indeterminate forms.

6

Review all tutor-marked assignments and address any areas of weakness.

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