Advanced Mathematics – Year 13 – Future Aerospace Engineering

About Course

Course Overview: Dive into advanced mathematical topics and build a strong foundation for university-level studies. This course covers topics in calculus, linear algebra, discrete mathematics, statistics, and more, equipping you with essential skills for further education and beyond.

Course Content

Lesson 1: Course Introduction and Objectives
o Welcome to the course and understand its structure.

Lesson 2: Real Analysis and Limits
o Study limits, continuity, and differentiability of functions. o Explore the Mean Value Theorem and applications.

Lesson 3: Sequences and Series
o Analyze sequences and series, including convergence tests. o Study power series and Taylor series.

Lesson 4: Vector Spaces and Linear Transformations
o Explore vector spaces, subspaces, and linear transformations. o Study matrices, determinants, and eigenvalues.

Lesson 5: Inner Product Spaces and Orthogonality
o Introduce inner product spaces and orthonormal bases. o Analyze applications of inner product spaces.

Lesson 6: Graph Theory and Algorithms
o Introduce graph theory, graphs, and graph algorithms. o Study graph connectivity and applications.

Lesson 7: Combinatorics and Counting Techniques
o Explore combinatorial methods, permutations, and combinations. o Analyze binomial coefficients and the Pigeonhole Principle.

Lesson 8: Complex Analysis and Contour Integration
o Study complex functions, Cauchy's theorem, and contour integration. o Explore applications in physics and engineering.

Lesson 9: Ordinary Differential Equations
o Analyze first-order and second-order ODEs. o Study techniques for solving linear and nonlinear ODEs.

Lesson 10: Probability Distributions and Statistical Inference
o Explore probability distributions, expected values, and variance. o Study statistical inference and hypothesis testing.

Lesson 11: Bayesian Statistics and Decision Theory
o Introduce Bayesian probability and decision theory. o Analyze applications in decision-making and parameter estimation.

Lesson 12: Numerical Analysis and Approximation
o Study numerical methods for solving equations and integration. o Analyze error analysis and convergence.

Lesson 13: Mathematical Modeling and Applications
o Explore mathematical modeling in various fields. o Study optimization, differential equations, and simulations.

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Advanced Mathematics – Year 13

About Course

What Will You Learn?

Course Content

Lesson 1: Course Introduction and Objectives o Welcome to the course and understand its structure.

Lesson 2: Real Analysis and Limits o Study limits, continuity, and differentiability of functions. o Explore the Mean Value Theorem and applications.

Lesson 3: Sequences and Series o Analyze sequences and series, including convergence tests. o Study power series and Taylor series.

Lesson 4: Vector Spaces and Linear Transformations o Explore vector spaces, subspaces, and linear transformations. o Study matrices, determinants, and eigenvalues.

Lesson 5: Inner Product Spaces and Orthogonality o Introduce inner product spaces and orthonormal bases. o Analyze applications of inner product spaces.

Lesson 6: Graph Theory and Algorithms o Introduce graph theory, graphs, and graph algorithms. o Study graph connectivity and applications.

Lesson 7: Combinatorics and Counting Techniques o Explore combinatorial methods, permutations, and combinations. o Analyze binomial coefficients and the Pigeonhole Principle.

Lesson 8: Complex Analysis and Contour Integration o Study complex functions, Cauchy's theorem, and contour integration. o Explore applications in physics and engineering.

Lesson 9: Ordinary Differential Equations o Analyze first-order and second-order ODEs. o Study techniques for solving linear and nonlinear ODEs.

Lesson 10: Probability Distributions and Statistical Inference o Explore probability distributions, expected values, and variance. o Study statistical inference and hypothesis testing.

Lesson 11: Bayesian Statistics and Decision Theory o Introduce Bayesian probability and decision theory. o Analyze applications in decision-making and parameter estimation.

Lesson 12: Numerical Analysis and Approximation o Study numerical methods for solving equations and integration. o Analyze error analysis and convergence.

Lesson 13: Mathematical Modeling and Applications o Explore mathematical modeling in various fields. o Study optimization, differential equations, and simulations.