Analysis 1 (Group 8)
Time: Friday 9-10am
Venue: Norfolk Building G.01 (The entrance of this building is on Surrey Street, See Here )
Definition, Monotone Convergence Theorem,
Sandwich Theorem, Algebra of Limits, Ratio Trick
Accumulation Points,
limsup and liminf (and Common Misconceptions)
Convergence Tests:
Comparison, Ratio, Root and Integral
Continuous and Distinuous Funtions , Finding Delta
Intermediate Value Theorem,
Extreme Value Theorem
Definition, Examples and Non-Examples,
Special Functions (Exotic Sine Curve & Cacuhy 1823)
Mean Value Theorems: Statement, Derivative Test, Curve Sketching,
Analytic Functions: Analyticity Lemma
Uniform Convergence and its Applications ,
Revision Exercises
Cauchy's MVT , Taylor's Theorem,
Power Series (Radius of Convergence and Applications)
The Fundamental Theorem of Calculus
Riemann's Integrals and Their Properties