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MTH112Sciences2 Unitsintermediate

Differential Calculus

This course, Differential Calculus, introduces fundamental concepts and techniques. It covers real numbers, functions, limits, continuity, and differentiation. Students will learn to differentiate various functions, including algebraic, trigonometric, and hyperbolic functions. Applications include curve sketching, optimization, and rate problems. Emphasis is placed on problem-solving and application, equipping students with essential calculus skills for mathematics, science, engineering, and economics.

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150h
Study Time
13
Weeks
12h
Per Week
advanced
Math Level
Course Keywords
Differential CalculusDifferentiationLimitsFunctionsCurve Sketching

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
Hands-on Practice

Course Topics

Key areas covered in this course

1

Real Numbers

2

Functions

3

Limits

4

Continuity

5

Differentiation

6

Curve Sketching

7

Optimization

8

Rate Problems

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

Computer Based Test

Career Opportunities

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Data Analyst

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Financial Analyst

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Engineer

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Statistician

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Economist

Apply your skills in this growing field

Industry Applications

Real-world sectors where you can apply your knowledge

FinanceEngineeringEconomicsComputer SciencePhysics

Study Schedule Beta

A structured 13-week journey through the course content

Week
1

Module 1:

6h

Unit 1: Basic Properties of Real Number

3 study hours
  • •Review the definition of sets and their notations.
  • •Study the different types of real numbers: natural, integers, rational, irrational, and real numbers.
  • •Understand the basic axioms of real numbers: field axioms and order axioms.
  • •Solve problems involving intervals and absolute values.

Unit 2: Basic Properties of Real Numbers

3 study hours
  • •Solve inequalities and represent solutions using intervals.
  • •Practice problems involving absolute values and their properties.
  • •Work through tutor-marked assignments to reinforce understanding.
Week
2

Module 1:

4h

Unit 3: Characteristics of Functions

4 study hours
  • •Define a function and identify its domain and range.
  • •Study the different types of functions: constant, polynomial, algebraic, and transcendental.
  • •Learn about exponential and logarithmic functions and their properties.
  • •Sketch graphs of basic elementary functions.
Week
3

Module 1:

4h

Unit 4: Limits

4 study hours
  • •Investigate the characteristics of functions: even, odd, periodic, monotonic, and bounded.
  • •Define and identify inverse functions.
  • •Define and construct composite functions.
  • •Determine whether a function has an inverse.
Week
4

Module 1:

5h

Unit 5: Algebra of Limits

5 study hours
  • •Study the formal definition of a limit of a function.
  • •Prove that the limit of a function is unique.
  • •Evaluate the limit of a function using various techniques.
  • •Evaluate right-hand and left-hand limits.
  • •Use the epsilon-delta method to prove that a number is the limit of a function.
Week
5

Module 2:

5h

Unit 1: Algebra of Limits

5 study hours
  • •State and apply theorems on limits: sum, product, and quotient theorems.
  • •Evaluate limits of functions using the sum, product, and quotient theorems.
  • •Evaluate limits of functions as x approaches infinity and negative infinity.
  • •Work through examples involving algebraic manipulation to find limits.
Week
6

Module 2:

4h

Unit 2: Differentiation

4 study hours
  • •Define a continuous function at a point.
  • •Recall properties of continuous functions.
  • •State theorems on continuous functions.
  • •State the three conditions for continuity of a function at a given point.
  • •Identify points of continuity and discontinuity of a function.
Week
7

Module 2:

5h

Unit 3: Rules for Differentiation I

5 study hours
  • •Define the slope of a point on a curve.
  • •Define the derivative of a function at a given point.
  • •Evaluate the derivative of a function using the limiting process (delta process or from first principles).
  • •Derive standard formulas for differentiation of polynomials.
  • •Find the derivative of polynomial functions using the delta process or a standard formula.
Week
8

Module 2:

5h

Unit 4: Rules for Differentiation II

5 study hours
  • •Derive the following rules for differentiation: sum rule, difference rule, product rule.
  • •Differentiate all types of polynomial functions using these rules.
  • •Practice applying the product rule and quotient rule to various functions.
  • •Solve problems involving combinations of differentiation rules.
Week
9

Module 3:

5h

Unit 1: Further Differentiation

5 study hours
  • •Apply the chain rule to differentiate composite functions.
  • •Differentiate logarithmic functions.
  • •Carry out logarithmic differentiation.
  • •Differentiate exponential functions.
  • •Find the derivative of the function a^u.
Week
10

Module 3:

5h

Unit 2: Differentiation of Logarithmic Functions and Exponential Function

5 study hours
  • •Differentiate trigonometric functions: sin x, cos x, tan x, etc.
  • •Differentiate inverse trigonometric functions: arcsin x, arccos x, arctan x, etc.
  • •Differentiate hyperbolic functions: sinh x, cosh x, tanh x, etc.
  • •Differentiate inverse hyperbolic functions.
Week
11

Module 3:

4h

Unit 3: Differentiation of Trigonometric 41 Functions

4 study hours
  • •Use the first derivative to determine where a curve is increasing, decreasing, or stationary.
  • •Use the second derivative to determine where a curve is concave upwards or concave downwards.
  • •Identify points of inflection.
  • •Sketch curves using information from the first and second derivatives.
Week
12

Module 3:

4h

Unit 4: Differentiation Inverse Trigonometric Functions and Hyperbolic Functions

4 study hours
  • •Define global and local minimum and maximum values.
  • •Apply differentiation to solve maximum and minimum problems.
  • •Solve rate problems using differentiation.
  • •Work through examples involving optimization and related rates.
Week
13

Module 4:

4h

Unit 1: Curve Sketching

4 study hours
  • •Use differentials to approximate values of functions.
  • •Apply differentiation to calculate velocity and acceleration of moving bodies.
  • •Solve problems involving approximations, velocity, and acceleration.
  • •Review all tutor marked assignments.

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 all definitions and theorems related to limits, continuity, and differentiation.

2

Practice solving a wide variety of problems from each unit, focusing on applying the rules of differentiation.

3

Create concept maps linking different types of functions and their derivatives.

4

Pay close attention to the epsilon-delta definition of limits and practice applying it to simple functions.

5

Focus on understanding the applications of differentiation, such as curve sketching, optimization, and rate problems.

6

Review all tutor-marked assignments (TMAs) and ensure you understand the solutions.

7

Practice time management during study sessions to simulate exam conditions.

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