Elementor #2629

Resource	Description	/
Required Book	Anton, H., Bivens, I. & Davis, S. (2012) Calculus 10th Edition – John Wiley & Sons, Inc.	/
Recommended Reading	Bird, J. (2021) Bird’s Higher Engineering Mathematics 9th Edition – Routledge Taylor & Francis Group	/
Other Resources	Online sources and journals YouTube tutorials	/
Week	Topic	Chapters on Book
Introductory Sessions	Introduction to the Course Explanation of course content & syllabus Recap on Fundamental Algebra Concepts Review on Basic Algebra Rules Definition of a Function and its Variables Graphs of Functions Geometric Effects on the Graphs of Functions Inverse Functions Operations on Functions Review on Differentiation	3Chapter 0
1 2 3	TRANSCENDENTAL FUNCTIONS Introduction to Transcendental Functions Main Classifications of Functions Algebraic Functions Definition of Transcendental Functions Types of Transcendental Functions Trigonometric Functions and their Inverses Basic Definitions of Trigonometric Functions Graphs of Trigonometric Functions Trigonometric Identities Derivatives of Trigonometric Functions Inverse Trigonometric Functions Derivatives of Inverse Trigonometric Functions Hyperbolic Functions and their Inverses Basic Definitions of Hyperbolic Functions Graphs of Hyperbolic Functions Hyperbolic Identities Derivatives of Hyperbolic Functions Inverse Hyperbolic Functions Derivatives of Inverse Hyperbolic Functions Exponential and Logarithmic Functions Basic Definitions of Exponential Functions Basic Definitions of Logarithmic Functions Natural Exponential Function Natural Logarithmic Function Properties of Exponential and Logarithmic Functions Relationship Between Exponential and Logarithmic Functions Derivatives of Exponential and Logarithmic Functions Applications of Transcendental Functions L’Hopital’s Rule Recap on Limits Types of Indeterminate Forms	Chapter 6
5	The Derivatives as a Function Slope, Lines and Tangent Lines. Tangents and Derivatives. Derivative of a Function using Definition. Other Notation and Higher Derivatives.	5
6	Derivatives of Trigonometric Functions, The Chain Rule Differentiation Formula for Special Functions. Rules of Differentiation. Review of Trigonometric Functions. Derivative of Basic Trigonometric Functions. Derivative of Functions involving Trigonometric Functions.	6
7	Implicit Differentiation Differentiation of Problems involving both ‘x’ and ‘y’.	7
8	Derivatives of Inverse Functions and Logarithms, Inverse Trigonometric Functions Inverse Functions Logarithms. Derivative of Inverse Functions. Logarithmic Differentiation. Derivative of Basic Inverse Trigonometric Functions. Derivative of Functions that involve Inverse Trigonometric Functions.	8
9	Related Rates, Linearisation and Differentials Derivative as Rate of Change. Related Rates. Linear Approximation.	9
10	Midterm Revision Sessions	1-9
11	Anti-Derivatives Calculation of Anti-Derivatives of a Function. Word Problems involving Physics/ Real-Life Scenarios.	10
12	The Definite Integral, The Fundamental Theorem of Calculus Definition of the Integral. Difference between Differentiation and Integration. Properties of Integral. Differentiation and Integration as Inverse Processes.	11
13	Indefinite Integrals, The Substitution Method Difference between Definite & Indefinite Integrals. Integration by Substitution Method.	12
14	Substitution and Area Between Curves, Extreme Values of Functions Determination of Maximum & Minimum Values of a Function. Local Minima/ Maxima. Global Minima/ Maxima. The Extreme Value Theorem.	13
15	Monotonic Functions & 1^st Derivative Test, Concavity & Curve Sketching Definition of Monotonic Function. Increasing & Decreasing Function. Concave-Upward, Concave-Downward & No-Curvature of Slope of a Function. Curve Sketching of a Function.	14
16	Applied Optimisation Problems on Optimisation of Area, Perimeter by Function Values Optimisation.	15
17	Final Exam Revision Sessions	10-15

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