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MCD 4490-Advanced Mathematics - Coggle Diagram
MCD 4490-Advanced Mathematics
Functions and Graphs
Linear Functions
Power Functions
Hyperbola and Truncus
Absolute Function
Hybrid Functions
Odd and Even Functions
Polynomials
Circular Functions
Trigonometric Identities
General solutions of trigonometric equations
Inverse Circular Functions
Graphs of Inverse Circular Functions
sin, cos, tan, sec, cosec, cot
Graphs of Circular Functions
Exponential and Logarithmic Functions
Index Laws
Exponential Equations
Graphs of Exponential Functions
Log Laws
Logarithmic Equations
Graphs of Logarithmic Functions
Applications of Exponential and Logarithmic Functions
Complex Numbers
Cartesian, Polar and Exponential forms
Operations of Complex Numbers
Solving Complex Equations
Argand diagrams
Locus and Subsets of Complex plane
Calculus
Differentiation
Differentiation of basic functions
Differentiation Rules (Product, Quotient, Chain)
Implicit and Logarithmic Differentiation
Higher Derivatives
Applications of Differentiation
i. Maximum Minimum Problems
ii. Kinematics
iii. Related rate of change problems
iv. Graph sketching
Integration
Integration of basic functions
Integration by substitutions
Integration by partial fractions
Integration by parts
Applications of Integration
i. Area under and between curves
ii. Volume formed by revolution
iii. Centre of mass of linear objects
iv. Mean value and Root mean square
v. Kinematics
Limits and Continuity
Differential Equations and Vector Functions
Solving 1st order linear differential equations
Applications to solve rate of change problems
Vector functions
Position, Velocity and Acceleration of moving objects
Cartesian equations of path of moving objects
Vectors
Definition and Examples
Vector Algebra
Vector dot(scalar) product
Scalar and Vector Projections
Applications of Vectors