This book is aimed at undergraduate students on their first year of a modular mathematics degree course. The important aims and objectives are presented clearly and reinforced using complete worked solution within the text. There is a natural increase in difficulty and understanding as each chapter progresses, always building upon the basic elements. The early chapters cover matrix algebra, vector algebra and complex numbers. Subsequent chapters cover such topics as real variable calculus, partial differentiation and multiple integrals. The concluding chapter motivates the students learning by consideration of applications taken from both physical and economic contexts.

1 Simultaneous Linear Equations 2 Vector Algebra 3 Complex Numbers 4 Review of Differentiation Techniques 5 Review of Integration Techniques 6 Applications of Differentiation 7 Partial Differentiation 8 Multiple Integrals 9 Differential Equations Solutions to Exercises

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