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2022 S1 Assignments |
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| Assignment 1 | 277 K |
| Assignment 1: Solutions | 309 K |
| Assignment 2 | 305 K |
| Assignment 2: Solutions | 310 K |
| Assignment 3 | 281 K |
| Assignment 3: Solutions | 294 K |
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2022 S1 Course Information |
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| Course Outline | 151 K |
| MATH201 Zoom Details | 75 K |
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2022 S1 Lecture Notes |
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| Chapter 1: Introduction, Logic, and Proof | 232 K |
| Chapter 2: The Real Numbers | 373 K |
| Chapter 3: Sequences and Series | 447 K |
| Chapter 4: Functions, Limits, and Continuity | 363 K |
| Chapter 5: The Derivative | 393 K |
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2022 S1 Lectures |
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| Lecture 1: Introduction (What is real analysis? + motivating examples) | 159131 K |
| Lecture 2: Logic (mathematical statements, compound statements, truth tables) | 147336 K |
| Lecture 3: Quantifiers (the quantifiers 'for all' and 'there exists', negating quantifiers) | 74238 K |
| Lecture 4: Proof (common proof strategies and examples) | 108725 K |
| Lecture 5: The Real Numbers (what is a number? set of rational numbers have holes, axiomatic definition of real numbers) | 135717 K |
| Lecture 6: The Ordering Axiom (ordering on natural numbers, intervals, bounded sets) | 83483 K |
| Lecture 7: The Completeness Axiom (sup and inf, completeness axiom, Archimedean property) | 119382 K |
| Lecture 8: Applications of Completeness Axiom (density of rationals, existence of square root, nested intervals theorem) | 109925 K |
| Lecture 9: The Real Numbers are Uncountable (rationals are countable but reals are not, max and min, examples) | 76940 K |
| Lecture 10: Open Sets (open sets, open intervals are open, examples, closed sets) | 122495 K |
| Lecture 11: Closed Sets (examples of closed sets, the absolute value, the triangle inequality) | 119536 K |
| Lecture 12: Convergence (Introduction to limits, definition of convergence, how to prove convergence) | 90945 K |
| Lecture 13: The Algebra of Limits (examples of limits, uniqueness of limits, statement of algebra of limits theorem) | 109281 K |
| Lecture 14: The Squeeze Theorem (proof of Algebra of limits, statement of Squeeze theorem, examples) | 116855 K |
| Lecture 15: Divergence (proof of Squeeze Theorem, divergence, examples of diverging sequences) | 78729 K |
| Lecture 16: Monotone Convergence (bounded sequences, monotone sequences, monotone convergence theorem, subsequences) | 120409 K |
| Lecture 17: Subsequences (subsequences and convergence, applications of monotone convergence) | 111942 K |
| Lecture 18: The Bolzano-Weierstrass Theorem (Bounded sequences have convergent subsequences, definition of Cauchy sequences, Cauchy sequences and convergence) | 118580 K |
| Lecture 19: Cauchy Sequences (proof of convergence of Cauchy sequence, convergence of series, the geometric series) | 120308 K |
| Lecture 20: Series (convergence of series vs convergence of sequences, harmonic series, alternating series test) | 112122 K |
| Lecture 21: Ratio Test (absolute convergence, comparison test, ratio test, Riemann rearrangement theorem) | 76167 K |
| Lecture 22: Limits and functions (outline of ch4, definition of limit, examples, limits of functions via limits of sequences) | 106517 K |
| Lecture 23: Functional Limits via Sequences (functional limits vs sequential limits, algebra of limits and squeeze theorem for functions, non-existence of limits) | 108002 K |
| Lecture 24: Continuous Functions (Definition, algebra of limits, composition, polynomials are continuous, IVT) | 100541 K |
| Lecture 25: Applications of IVT (flipped IVT, examples, Nth root, irrational roots) | 108401 K |
| Lecture 26: The Extreme Value Theorem (motivation, proof of EVT, pointwise convergence for sequences of functions, examples) | 107928 K |
| Lecture 27: Uniform Convergence | 79168 K |
| Lecture 28: The Derivative (Definition, examples, continuous vs differentiable, product and quotient rules) | 91650 K |
| Lecture 29: Manipulating Derivatives (Chain rule, derivatives are local, applications, intro to MVT) | 94001 K |
| Lecture 30: The Mean Value Theorem (MVT, derivative zero at max/min, Rolle's Theorem, applications) | 105972 K |
| Lecture 31: Taylor's Theorem (higher order derivatives, generalised Rolle's Theorem, Taylor's Theorem, examples) | 88772 K |
| Lecture 32: Power Series (exponential function, power series, basic properties, radius of convergence) | 93217 K |
| Lecture 33: Power Series II (differentiability of power series, swapping derivatives and limits) | 99500 K |
| Lecture 34: The Integral (partitions, upper and lower Riemann sums, Riemann integrable functions, Fundamental Theorem of Calculus) | 96334 K |
| Lecture 35: Review Lecture | 84043 K |
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2022 S1 Practice Exam |
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| 2022 MATH201 practice exam | 289 K |
| MATH201 exam front page 2022 | 255 K |
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2022 S1 Test |
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| Information on Test | 81 K |
| MATH201 Test 2022 | 255 K |
| MATH201 Test 2022: Solutions | 251 K |
| Practise test: Solution to Part B, Q1 | 1320 K |
| Practise Test | 122 K |
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2022 S1 Tutorial Problems |
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| Tutorial 1 (sets, truth tables, negation, proof) | 134 K |
| Tutorial 1: Solutions | 131 K |
| Tutorial 2 (sup and inf) | 111 K |
| Tutorial 2: Solutions | 161 K |
| Tutorial 3 (max and min, open and closed sets) | 125 K |
| Tutorial 3: Solutions | 142 K |
| Tutorial 4 (triangle inequality, limits of sequences) | 159 K |
| Tutorial 4: Solutions | 189 K |
| Tutorial 5 (diverging sequences, increasing and decreasing sequences, subsequences) | 137 K |
| Tutorial 5: Solutions | 161 K |
| Tutorial 6 (sequences, subsequences, monotone convergence) | 131 K |
| Tutorial 6: Solutions | 145 K |
| Tutorial 7 (convergence of series) | 155 K |
| Tutorial 7: Solutions | 178 K |
| Tutorial 8 (Limits for functions) | 121 K |
| Tutorial 8: Solutions | 146 K |
| Tutorial 9 (continuous functions, IVT, EVT)) | 136 K |
| Tutorial 9: Solutions | 156 K |
| Tutorial 10 (differentiable functions) | 148 K |
| Tutorial 10: Solutions | 163 K |
| Tutorial 11 (higher order derivatives, MVT, Taylor's theorem) | 129 K |
| Tutorial 11: Solutions | 149 K |
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Private Tutoring for 2022 |
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| Download the list of private tutors |
