MA1301 (Lecture Slides)2019 Chapter1.pdf - Introduction Contents Workload Sequences Introduction 2 44 What we will learn in MA1301 Introduction Contents

MA1301 (Lecture Slides)2019 Chapter1.pdf - Introduction...

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IntroductionIntroductionContentsWorkloadSequences2 / 44
What we will learn in MA1301IntroductionContentsWorkloadSequences3 / 44This is equivalent toGCE A-level mathematics. Major topics:Sequences:a1, a2, a3, . . .,a1+a2+a3+· · ·.(Generalized) Binomial theorem.Mathematical induction.Derivative & Its Applications:ddxf(x).Linear approximation, Curve plotting,Connected rate of change, Optimization problem.Integral & Its Applications:f(x)dxandbaf(x)dx.Area problem, Volume problem.Ordinary differential equation.
What we will learn in MA1301IntroductionContentsWorkloadSequences4 / 44This is equivalent toGCE A-level mathematics. Major topics:Vectors:ai+bj+ck.Three-dimensional vector space.Vector products.Points, Lines, Planes, Angles, Distances.Complex Numbers:a+bi, where theimaginary unitisatisfiesi2=1.Arithmetic & Geometric properties of complex numbers.You will be equipped with essential mathematical skills andknowledge for your further study in mathematics.
SequencesIntroductionSequencesSequenceArithmetic SequenceSum of ArithmeticSequencesGeometric SequenceSum of GeometricSequenceLimit of SequenceSum to Infinity ofGeometric SequenceTelescoping SumBinomial TheoremGeneralized BinomialTheoremMathematical Induction7 / 44
SequenceIntroductionSequencesSequenceArithmetic SequenceSum of ArithmeticSequencesGeometric SequenceSum of GeometricSequenceLimit of SequenceSum to Infinity ofGeometric SequenceTelescoping SumBinomial TheoremGeneralized BinomialTheoremMathematical Induction8 / 44Asequenceis a list of numbers in definite order:a1, a2, a3, . . . , an,. . . . . .anis called thenthtermof the sequence.Example:1,2,3,4, . . . , n, n+ 1,. . . . . .The sequence ofpositive integers:a1= 1, a2= 2, a3= 3, . . . , an=n, . . .Thesetofpositive integersis denoted byZ+.Zcomes from German “Zahlen” (for numbers).The upper subscript+refers to “positive”.In short form, the sequence of positive integers is{an}, wherean=nfor allnZ+.
SequenceIntroductionSequencesSequenceArithmetic SequenceSum of ArithmeticSequencesGeometric SequenceSum of GeometricSequenceLimit of SequenceSum to Infinity ofGeometric SequenceTelescoping SumBinomial TheoremGeneralized BinomialTheoremMathematical Induction9 / 44A sequencea1, a2, . . . , an, . . .is represented as{an},whereanis the expression of thenthterm.Example: Find thenthterm of the following sequence.1,3,5,7,9,. . . . . .a1= 1;a2= 1 + 2;a3= 1 + 2×2;a4= 1 + 2×3;a5= 1 + 2×4;.............................................................an= 1 + 2×(n1) = 1 + (2n2) =2n1.12,32,52,72,92,. . . . . .an=(2n1)2
Arithmetic SequenceIntroductionSequencesSequenceArithmetic SequenceSum of ArithmeticSequencesGeometric SequenceSum of GeometricSequenceLimit of SequenceSum to Infinity ofGeometric SequenceTelescoping SumBinomial TheoremGeneralized BinomialTheoremMathematical Induction10 / 44A sequencea1, a2, . . . , an, . . .

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