DAY 26 Laplace Transforms (p 252 - 257 8th ed)Let f(t) be a function of t defined for each positive values of t. Then the Laplace transform of f(t), denoted by provided that the integral exists. s is a parameter, which may be a real or complex number. being clearly a function of s is briefly written as f(s). Find the Laplace Transforms of the following:

14.1/253 L{ekt}

Evaluate:6/256L{e-2t + 4e-3t + 3}

7/256 L{3e4t e-2t}

DAY 26 Laplace Transforms (p 252 - 257 8th ed)Let f(t) be a function of t defined for each positive values of t. Then the Laplace transform of f(t), donated by provided that the integral exists. s is a parameter, which may be a real or complex number. being clearly a function of s is briefly written as F(s). Find the Laplace Transforms of the following:

14.1/253 L{ekt}

14.2/254 L{sinkt} p254 for formula

Evaluate:L{-3sin3t + 4cos2t + 2e4t + 5}

2. L{6cosh3t 2sin4t + 6e2t}

DAY 26 Laplace Transforms (p 252 - 257 8th ed)Let f(t) be a function of t defined for each positive values of t. Then the Laplace transform of f(t), donated by provided that the integral exists. s is a parameter, which may be a real or complex number. being clearly a function of s is briefly written as F(s). Find the Laplace Transforms of the following:

14.1/253 L{ekt}

14.2/254 L{sinkt} p254 for formula

14.3/254 L{tn} for n positive integerEvaluate:4/256L{t2 +4t 5e-5t}

5/256L{t3 t2 + 4t 3sin2t +2cosh4t}

1. f(t) = 2e2t 3 sin 3t + 7 cosh2t + 5t3

DAY 26 Laplace Transforms (p 252 - 257 8th ed)

DAY 26 Laplace Transforms (p 252 - 257 8th ed)Refer to Page 318 319 for Table of TransformsExample: Find the Laplace transform of the following:f(t) = e3tt3

f(t) = e2t sin 4t

F(t) =e4t cosh 3t

(refer to page 256 257 8th ed for other exercises)

DAY 26 Laplace Transforms (p 252 - 257 8th ed)Refer to Page 318 319 for Table of Transforms

DAY 27 Inverse Transforms (p 274 277 8th ed)

DAY 27 Inverse Transforms (p 274 277 8th ed)Evaluate the following:

DAY 27 Inverse Transforms (p 274 277 8th ed)Theorem 15.2 page 276

L-1[f(s)} = e-at L-1{f(s a)}Note: More exercises on page 276 277 8th edExample:

15.1/ 276 Find L-1 {15/ (s2 +4s +13)}

15.2/ 276 Find L-1 {(s + 1)/ (s2 + 6s + 25)}

POINTERS FOR PRESENTATION Sept 5, 2011: (10 points in Q3 over and above your scores but not greater than 100 points)

Use powerpoint and include the following information:Title Page (Group Number, Section and Names)ProblemSolutionSchematic DiagramGraphic OrganizerStep-by-step DocumentationJournalVideo Presentation will be assigned as HW 6 (20 points)Tarpaulin will be for the top 5 groups that will be chosen to compete for the additional points in the final exams

NOTE:Each group will be given maximum of 15 mins for presentation, each member should be given equal opportunity to discuss. If one of the group member is absent then he will not be given the additional point.Use your own equipment for presentation.Submit your project and the softcopy of your powerpoint presentation.

Rubric for Group Oral Presentation

Oral PresentationExcellent10 - 8Satisfactory7.9 5Needs Improvement4.9 1OrganizationStudent presents information in logical interesting sequence which audience can follow.Student presents information in logical sequence which audience can follow.Audience cannot understand presentation because there is no sequence of information.Content KnowledgeStudent demonstrates full knowledge (more than required) with explanations and elaborations.Students is at ease with content, but fails to elaborate.Student does not have a grasp of information, student cannot answer questions about subject.VisualsStudents used appropriate visuals to reinforce text and presentation.Visuals used are related to text and presentation.Student used no visuals.MechanicsPresentation has no misspellings or grammatical errors.Presentation has no more than two misspellings and/or grammatical error.Students presentation had three or more spelling errors and/or grammatical errors.DeliveryStudent used a clear voice and correct, precise pronunciation of terms and with pleasing appearance.Students voice is clear. Student pronounces most words correctly and somehow presentable.Student mumbles, incorrectly pronounces terms, and speaks too quietly for students in the back of class to hear.

Criteria for the best project that will qualify for the additional points in the final exams. (Only three groups in all the DE class)

Paper 15%Presentation 30%Project Output 40%Video Presentation 15%

Note:The group should obtain at least 10/10 for the presentation and 20/20 for the video presentation to qualify.

The additional points in the final exam is irrespective of your raw score.

Rubric for Group Process

Group ProcessExcellent8 - 10Satisfactory5 7.9Needs Improvement1 4.9Level of ParticipationEach member was equally involved in the process.Most members were active in the process.One or two members dominated discussion and led the process.Cooperative EffortThere was evidence that each member contributed to the final product.Most members contributed to the final product.One or two members completed the final product.ListeningMembers made eye contact with the speaker. Body movement kept to a minimum by all.Most members attended to the speaker.Members did not attend to the speaker and seemed intent on speaking over others.On-task behaviorDiscussion was on the topic with no distractions notedSome off-task behavior was noted, but group members got one another right back on task.Much off-task discussion occurred. Group had to be brought back on task by others.InteractionsWords of politeness noted. Very few interruptions.Polite words were often used. Some interruptions and impulsive behavior noted.Group members behaved impulsively; polite words were not in evidence.

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