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MTH102Sciences3 Unitsintermediate

Elementary Mathematics II

This course introduces differential and integral calculus, demonstrating their application in contemporary business, technology, and science. It equips learners with essential mathematical skills for science and engineering, emphasizing the use of mathematical techniques to solve real-world problems. Learners will integrate mathematical models in sciences and engineering, enhancing their proficiency in calculus and its practical applications.

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91h
Study Time
13
Weeks
7h
Per Week
advanced
Math Level
Course Keywords
FunctionsLimitsDifferentiationIntegrationCalculus

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

Functions and Graphs

2

Limits and Continuity

3

Differentiation Techniques

4

Applications of Derivatives

5

Integration Techniques

6

Volumes of Revolution

Total Topics6 topics

Requirements

Knowledge and skills recommended for success

MTH101 - Elementary Mathematics I

💡 Don't have all requirements? Don't worry! Many students successfully complete this course with basic preparation and dedication.

Assessment Methods

How your progress will be evaluated (2 methods)

Tutor Mark 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

Engineer

Apply your skills in this growing field

Data Analyst

Apply your skills in this growing field

Financial Analyst

Apply your skills in this growing field

Statistician

Apply your skills in this growing field

Applied Mathematician

Apply your skills in this growing field

Industry Applications

Real-world sectors where you can apply your knowledge

EngineeringFinanceData SciencePhysicsComputer Science

Study Schedule Beta

A structured 13-week journey through the course content

Week
1

MODULE 1: FUNCTIONS

7h

Unit 1: Function and Graphs

7 study hours
  • •Read the course guide.
  • •Familiarize yourself with course objectives and assessment methods.
  • •Understand the course structure and learning outcomes.
Week
2

MODULE 1: FUNCTIONS

7h

Unit 1: Function and Graphs

7 study hours
  • •Define functions and graphs.
  • •Describe the concept of graphs.
  • •Solve problems related to functions and graphs.
  • •Study different types of functions (polynomial, algebraic, transcendental).
Week
3

MODULE 1: FUNCTIONS

7h

Unit 2: Limits

7 study hours
  • •Define the limit of functions.
  • •Describe the concept of limit of functions.
  • •Solve problems related to the limit of functions.
  • •Understand right-hand and left-hand limits and theorems on limits.
Week
4

MODULE 1: FUNCTIONS

7h

Unit 3: Idea of Continuity

7 study hours
  • •Define continuity of functions.
  • •State continuity properties conditions.
  • •Define continuity of polynomial and rational functions.
  • •Study theorems on continuity and piecewise continuity.
Week
5

MODULE 2: CALCULUS OF DIFFERENTIATION

7h

Unit 1: The Derivative as Limit of Rate of Change

7 study hours
  • •Define rate of change of function.
  • •Solve differentiation from first principle.
  • •Solve differentiation from second principle.
  • •Understand right-hand and left-hand derivatives and differentiability in an interval.
Week
6

MODULE 2: CALCULUS OF DIFFERENTIATION

7h

Unit 2: Differentiation Technique

7 study hours
  • •Construct product of function.
  • •Solve problems on quotient of functions.
  • •Develop and solve implicit functions.
  • •Carry out solution on function of functions.
Week
7

MODULE 2: CALCULUS OF DIFFERENTIATION

7h

Unit 2: Differentiation Technique

7 study hours
  • •Continue working on differentiation techniques.
  • •Practice solving more complex problems.
  • •Review and consolidate understanding of different differentiation rules.
Week
8

MODULE 2: CALCULUS OF DIFFERENTIATION

7h

Unit 2: Differentiation Technique

7 study hours
  • •Complete differentiation techniques.
  • •Focus on mastering implicit functions and function of functions.
  • •Prepare for self-assessment exercises.
Week
9

MODULE 3: CALCULUS OF INTEGRATION

7h

Unit 1: Integration

7 study hours
  • •Describe the calculus integration of function.
  • •Apply basic integral theorem to functions.
  • •Evaluate change of variable in integration.
  • •Study properties of definite integrals and mean value theorems for integrals.
Week
10

MODULE 3: CALCULUS OF INTEGRATION

7h

Unit 1: Integration

7 study hours
  • •Continue working on integration techniques.
  • •Focus on standard integrals and methods of integration.
  • •Practice solving more complex integration problems.
Week
11

MODULE 3: CALCULUS OF INTEGRATION

7h

Unit 1: Integration

7 study hours
  • •Complete integration techniques.
  • •Focus on integrals of special functions and integration by partial fraction.
  • •Prepare for self-assessment exercises.
Week
12

MODULE 3: CALCULUS OF INTEGRATION

7h

Unit 2: Volume of Solids of Revolution by Definite Integral

7 study hours
  • •Find the arc length under integration.
  • •Determine the volume of solid revolution.
  • •Evaluate the volume of a sphere, spherical and cone.
  • •Study disk method and shell method for volumes of revolution.
Week
13

MODULE 3: CALCULUS OF INTEGRATION

7h

Unit 2: Volume of Solids of Revolution by Definite Integral

7 study hours
  • •Complete volume of solids of revolution.
  • •Focus on solving problems related to sphere, spherical segment, and cone.
  • •Review all module contents and prepare for final revision.

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 from each unit.

2

Practice solving a variety of problems from the self-assessment exercises.

3

Focus on understanding the underlying concepts rather than memorizing formulas.

4

Create concept maps linking differentiation and integration techniques.

5

Allocate sufficient time for revision and practice before the exam.

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