Lesson Plan


Week 1
Parametric Equations & Polar Coordinates: Parametric equations, polar coordinate system. Relationship between Cartesian and polar coordinates.
Week 2
Graphs of polar equation and intersections point in polar coordinates.
Week 3
Review: Graphs of trigonometric functions, exponential, trigonometric identities, and graphs of f and f –1 in general. Transcendental Functions: Hyperbolic functions, Inverse trigonometric functions, and inverse hyperbolic functions.
Week 4
Graphs of hyperbolic, hyperbolic inverses and trigonometric inverses. Identities of hyperbolic and trigonometric inverses, and solving related equations
Week 5
Differentiation (including implicit relation) of functions and relations involving hyperbolic and inverses.
Week 6
Integration of functions involving hyperbolic and inverses using definition, identities and integration by parts.
Week 7
Integration using substitution method, partial fraction, trigonometric and hyperbolic substitutions.
Week 8
Further Applications of Integration: Arc length, area of surface of revolution in Cartesian form.
Week 9
Arc length, area of surface of revolution in polar and parametric form.
Week 10
Improper Integrals. L’Hopital’s Rule, Integral of first kind
Week 11
Integral of second kind
Week 12
Multivariable Functions: Terminology and notation, domain and range of two and three variables functions. Graphs of two variable functions: Surfaces and level curves.
Week 13
Graphs of three variable functions: Level surfaces.
Week 14
Limits and continuity: Notions of limits and continuity for functions of two variables including non-existence of limits (two paths rule).