1. Elementary linear algebra: Vectors, linear independence, scalar product. Matrices, simultaneous equations, determinants, Gaussian elimination, eigenvalues, eigenvectors, applications. Equation of straight line & plane. 2. Introduction to proof-based calculus: Fields, sequences, limits, continuity, intermediate and extreme value theorems, maxima & minima. 3. Techniques of calculus: Series, differentiation, integration, numerical methods, Taylor series, L'Hopital's rule. This course differs from MATH1051 by treating material in more depth and with greater rigour.
| Week 1 - (2/23/2026 - 2/27/2026) |
Sets, fields, and sequences
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| Week 2 - (3/2/2026 - 3/6/2026) |
Limits of sequences, squeeze theorem, convergence
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| Week 3 - (3/9/2026 - 3/13/2026) |
Limsup, liminf, limit points, Cauchy sequences
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| Week 4 - (3/16/2026 - 3/20/2026) |
Limits of functions, continuity of functions
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| Week 5 - (3/23/2026 - 3/27/2026) |
Intermediate and extreme value theorems, differentiation
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| Week 6 - (3/30/2026 - 4/3/2026) |
Mean value theorem, optimisation, Riemann integral
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| Week 7 - (4/13/2026 - 4/17/2026) |
Integrability, MVT for integrals
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| Week 8 - (4/20/2026 - 4/24/2026) |
Fundamental theorem of calculus, indefinite integrals
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| Week 9 - (4/27/2026- 5/1/2026) |
Methods of integration, area below curves, series
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| Week 10 - (5/4/2026 - 5/8/2026) |
Convergence tests for series, Taylor and Maclaurin series
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| Week 11 - (5/11/2026 - 5/15/2026) |
Systems of linear equations, matrices
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| Week 12 - (5/18/2026 - 5/22/2026) |
Matrix inversion, determinants
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| Week 13 - (5/25/2026 - 5/29/2026) |
Eigenvalues, eigenvectors, vector spaces
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