第一部分 MCM 2013年A题 3
第一章 赛题：The Ultimate Brownie Pan 3
第二章 论文1：The Ultimate Brownie Pan 5
2.1 Introduction 6
2.2 Assumptions 7
2.3 Notations 8
2.4 Part Ⅰ 8
2.5 Part Ⅱ 18
2.6 Strengths and Weaknesses 22
2.7 Future Work 22
2.8 点评 23
第三章 论文2：The Ultimate Brownie Pan 24
3.1 Introduction 25
3.2 Problem Analysis 25
3.3 Assumptions 26
3.4 Models 27
3.5 Results 34
3.6 Analysis of Models 39
3.7 点评 40
第四章 论文3：The Ultimate Brownie Pan 41
4.1 Introduction 42
4.2 Restatement of the Problem 42
4.3 Problem Analysis 43
4.4 Model Assumptions 44
4.5 Model and Solution 44
4.6 Evaluation of the Model 61
4.7 Future Works 61
4.8 点评 62
第五章 论文4：Heat Distribution and the Ultimate Brownie Pan 63
5.1 Introduction 64
5.2 Heat Distribution Problem—the Models of Heat Distribution Across Pans 65
5.3 The Pan-Shape-Choosing Problem 78
5.4 点评 85
第六章 论文5：Ultimate Brownie Pan，Live in a Delicious Way 86
6.1 Introduction and Backgrounds 87
6.2 Terminology and Definitions 87
6.3 Assumptions 88
6.4 Temperature Distribution Model 89
6.5 Solutions to Requirements 96
6.6 Sensitivity Analysis 102
6.7 Strengths and Weaknesses 103
6.8 点评 104
第七章 论文6：The Ultimate Brownie Pan 105
7.1 Introduction 106
7.2 Assumptions 107
7.3 Heat Analysis 107
7.4 Unevenness of Distribution 112
7.5 Arrangement Problem 114
7.6 Weight Analysis 118
7.7 Sensitivity Analysis 121
7.8 Conclusions 121
7.9 Strengths and Weaknesses 122
7.1 0点评 123
第二部分 MCM 2011年A题 127
第八章 赛题：Snowboard Course 127
第九章 论文1：Research of the Snowboard Course 128
9.1 Introduction 128
9.2 Scheme 1 129
9.3 Scheme 2 133
9.4 Scheme 3 134
9.5 Strengths and Weaknesses 135
9.6 Conclusions 135
9.7 点评 136
第十章 论文2：Snowboard Course：the Optimization of the Halfpipe Shape 138
10.1 Introduction 139
10.2 Assumptions 141
10.3 Variable Definition 141
10.4 Analysis of the Problem 142
10.5 The Model Results 145
10.6 Improve the Model 148
10.7 Conclusions 149
10.8 Strengths and Weaknesses 150
10.9 点评 150
第十一章 论文3：A Solution to Snowboard Course 152
11.1 Introduction 153
11.2 Analysis 153
11.3 Variables and Assumption 156
11.4 Model 158
11.5 Model Optimization 166
11.6 Practical Application 168
11.7 Conclusion 169
11.8 Appendix 171
11.9 点评 171
第三部分 MCM 2010年A题 175
第十二章 赛题：The Sweet Spot 175
第十三章 论文1：Hit the ball，hit the sweet spot 176
13.1 Introduction 177
13.2 General Assumptions 178
13.3 The Collision Model 178
13.4 Two Definitions of the Sweet Spot 179
13.5 Verification of the Model 180
13.6 Corking the Bat 181
13.7 The Vertical Sweet Zone 185
13.8 Metal Bats 187
13.9 点评 189
第十四章 论文2：The Sweet Spot 190
14.1 Restatement of the Problem 191
14.2 Terms and Ambiguous Words 191
14.3 Ambiguous Words 191
14.4 Assumptions 191
14.5 The COP Model 192
14.6 The Plane-parallel Motion Model 193
14.7 The Plane-parallel Motion Model of a Corked Bat 199
14.8 Dynamics of Swinging a Bat 202
14.9 The Comprehensive Consideration 204
14.10 点评 206